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I 



THE ART OF LOGICAL THINKING 

OR 

THE LAWS OF REASONING 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



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THE ART OF 

LOGICAL THINKING 

OR 

THE LAWS OF REASONING 



By WILLIAM WALKER ATKINSON 



L. N. FOWLER & COMPANY 

1, Imperial Arcade, Ludgate Circus 

London, E. C, EuKland 



1909 

THE PROGRESS COMPANY 

CHICAGO. ILL. 






6^'^ 



Copyright 1909 

By 

THE PROGRESS COMPANY 

Cliicago, 111., U. S. A. 



5nj,Aa5 9i.os 



CONTENTS 



I. Reasoning 9 

II. The Process of Reasoning 17 

III. The Concept 25 

IV, The Use of Concepts 37 

V. Concepts and Images 48 

VL Terms 56 

VII. The Meaning of Terms 73 

VIIL Judgments 82 

IX. Propositions 90 

X. Immediate Reasoning 99 

XI. Inductive Reasoning 107 

XII. Reasoning by Induction 116 

XIII. Theory and Hypotheses 125 

XIV. Making and Testing Hypotheses 132 

XV. Deductive Reasoning 144 

XVL The Syllogism 156 

XVII. Varieties of Syllogisms 167 

XVIII. Reasoning by Analogy 179 

XIX. FaUacies 186 



CHAPTER I. 

REASONING 

'* Reasoning^ ^ is defined as: *^The act, 
process or art of exercising the faculty of rea- 
son ; the act or f actdty of employing reason in 
argument; argumentation, ratiocination; rea- 
soning power ; disputation, discussion, argu- 
mentation.*^ Stewart says: ^*The word rea- 
son itself is far from being precise in its mean- 
ing. In common and popular discourse it de- 
notes that power by which we distinguish 
truth from falsehood, and right from wrong, 
and by which we are enabled to combine means 
for the attainment of particular ends. ' * 

By the employment of the reasoning facul- 
ties of the mind we compare objects presented 
to the mind as percepts or concepts, taking up 
the **raw materials'' of thought and weaving 
them into more complex and elaborate mental 
fabrics which we call abstract and general 
ideas of truth, Brooks says : ^ ' It is the think- 
ing power of the mind ; the faculty which gives 
us what has been called thought-knowledge, in 



10 LoGicAii Thinking 

distinction from sense-knowledge. It may be 
regarded as the mental architect among the 
faculties ; it transforms the material furnished 
by the senses . . . into new products, and 
thus builds up the temples of science and phil- 
osophy. '^ The last-mentioned authority adds: 
^^Its products are twofold, ideas and thoughts. 
An idea is a mental product which when ex- 
pressed in words does not give a proposition ; 
a thought is a mental product which embraces 
the relation of two or more ideas. The ideas 
of the understanding are of two general 
classes ; abstract ideas and general ideas. The 
thoughts are also of two general classes ; those 
pertaining to contingent truth and those per- 
taining to necessary truth. In contingent 
truth, we have facts, or immediate judgments, 
and general truths including laws and causes, 
derived from particular facts; in necessary 
truth we have axioms, or self-evident truths, 
and the truths derived from them by reason- 
ing, called theorems/'. 

In inviting you to consider the processes of 
reasoning, we are irresistibly reminded of the 
old story of one of Moliere's plays in which 
one of the characters expresses surprise on 



Reasonikg 11 

learning that he ^ ' had been talking prose for 
forty years without knowing it. ' ' As Jevons 
says in mentioning this : ^ ' Ninety-nine people 
out of a hundred might be equally surprised 
on hearing that they had been converting 
propositions, syllogizing, falling into paralo- 
gisms, framing hypotheses and making classi- 
fications with genera and species. If asked 
whether they were logicians, they would prob- 
ably answer. No ! They would be partly right ; 
for I believe that a large number even of edu- 
cated persons have no clear idea of what logic 
is. Yet, in a certain way, every one must have 
been a logician since he began to speak.'' 

So, in asking you to consider the processes 
of reasoning we are not assuming that you 
never have reasoned— on the contrary we are 
fully aware that you in connection with every 
other person, have reasoned all your mature 
life. That is not the question. While every- 
one reasons, the fact is equally true that the 
majority of persons reason incorrectly. Many 
persons reason along lines far from correct 
and scientific, and suffer therefor and thereby. 
Some writers have claimed that the majority 
of persons are incapable of even fairly correct 



12 Logical Thinking 

reasoning, pointing to the absurd ideas enter- 
tained by the masses of people as a proof of 
the statement These writers are probably 
a little radical in their views and statements, 
but one is often struck with wonder at the 
evidences of incapacity for interpreting facts 
and impressions on the part of the general 
public. The masses of people accept the most 
absurd ideas as truth, providing they are 
gravely asserted by some one claiming author- 
ity. The most illogical ideas are accepted 
wjithout dispute or examination, providing 
they are stated solemnly and authoritatively. 
Particularly in the respective fields of relig- 
ion and politics do we find this blind accept- 
ance of illogical ideas by the multitude. Mere 
assertion by the leaders seems sufficient for 
the multitude of followers to acquiesce. 

In order to reason correctly it is not merely 
necessary to have a good intellect. An athlete 
may have the proper proportions, good frame- 
work, and symmetrical muscles, but he can- 
not expect to oope with others of his kind un- 
less he has learned to develop those muscles 
and to use them to the best advantage. And, 
in the same way, the man who wishes to reason 



Rbasonikg 13 

correctly must develop his intellectual facul- 
ties and must also learn the art of using them 
to the best advantage. Otherwise he will 
w-aste his mental energy and will be placed at 
a disadvantage when confronted with a 
trained logician in argument or debate. One 
who has witnessed a debate or argument be- 
tween two men equally strong intellectually, 
one of whom is a trained logician and the other 
lacking this advantage, will never forget the 
impression produced upon hitn by the unequal 
struggle. The conflict is like that of a power- 
ful wrestler, untrained in the little tricks and 
turns of the science, in the various principles 
of applying force in a certain way at a certain 
time, at a certain place, with a trained and ex- 
perienced wrestler. Or of a conflict between 
a muscular giant untrained in the art of box- 
ing, when confronted with a trained and ex- 
perienoed exponent of **the manly art.'* The 
result of any such conflict is assured in ad- 
vance. Therefore, everyone should refuse to 
rest content without a knowledge of the art 
of reasoning correctly, for otherwise he places 
himself under a heavy handicap in the race 
for success, and allows others, perhaps less 



14 Logical Thinking 

well-equipped mentally, to have a decided ad- 
vantage over him. 

Jevons says in this connection: *^To be a 
good logician is, however, far more valuable 
than to be a good athlete ; because logic teaches 
us to reason well, and reasoning gives us 
knowledge, and knowledge, as Lord Bacon 
said, is power. As athletes, men cannot for a 
moment compare with horses or tigers or 
monkeys. Yet, with the power of knowledge, 
men tame horses and shoot tigers and despise 
monkeys. The weakest framework with the 
most logical mind will conquer in the end; be- 
cause it is easy to foresee the future, to cal- 
culate the result of actions, to avoid mis- 
takes which might be fatal, and to discover the 
means of doing things which seemed impos- 
sible. If such little creatures as ants had bet- 
ter brains than men, they would either destroy 
men or make them into slaves. It is true that 
we cannot use our eyes and ears without 
geting some kind of knowledge, and the brute 
animals can do the same. But what gives 
power is the deeper knowledge called Science. 
People may see, and hear, and feel all 
their lives without really learning the na- 



Reasoning 15 

ture of things they see. But reason is the 
mind's eye, and enables us to see why things 
are, and when and how events may be made to 
happen or not to happen. The logician en- 
deavors to learn exactly what this reason is 
which makes the power of men. We all, as I 
have said, must reason well or ill, but logic is 
the science of reasoning and enables us to dis- 
tinguish between the good reasoning which 
leads to truth, and the bad reasoning which 
every day betrays people into error and mis- 
fortune. '^ 

In this volume we hope to be able to point 
out the methods and principles of correctly 
using the reasoning faculties of the mind, in a 
plain, simple manner, devoid of useless tech- 
nicalities and academic discussion. We shall 
adhere, in the main, to the principles estab- 
lished by the best of the authorities of the old 
school of psychology, blending the same with 
those advanced by the best authorities of the 
New Psychology. No attempt to make of this 
book a school text-book shall be made, for our 
sole object and aim is to bring this important 
subject before the general public composed of 



16 Logical Thinking 

people who have neither the time nor inclina- 
tion to indulge in technical discussion nor 
academic hair-splitting, but who desire to un- 
derstand the underlying working principles of 
the Laws of Reasoning. 



CHAPTER IL 

THE PKOCESS OF REASONING 

k 

The processes of Eeasoning may be said to 
comprise four general stages or steps, as 
follows : 

L Abstraction, by wMcb is meant the proc- 
ess of drawing off and setting aside from an 
object, person or thing, a quality or attribute, 
and making of it a distinct object of thought. 
For instance, if I perceive in a lion the quality 
of strength, and am able to think of this qual- 
ity abstractly and independently of the animal 
—if the term strength has an actual mental 
meaning to me, independent of the lion— then 
I have abstracted that quality; the thinking 
thereof is an act of abstraction; and the 
thought-idea itself is an abstract idea. Some 
writers hold that these abstract ideas are real- 
ities, and ^^not mere figments of fancy." As 
Brooks says : ^ ^ The rose dies, but my idea of 
its color and fragrance remains." Other au- 
thorities regard Abstraction as but an act of 
attention concentrated upon but the particu- 

17 



18 Logical Thinking 

lar quality to the exclusion of others, and that 
the abstract idea has no existence apart from 
the general idea of the object in which it is 
included. Sir William Hamilton says: ^^We 
can rivet our attention on some particular 
mode of a thing, as its smell, its color, its fig- 
ure, its size, etc., and abstract it from the oth- 
ers. This may be called Modal Abstraction. 
The abstraction we have now been considering 
is performed on individual objects, and is con- 
sequently particular. There is nothing neces- 
sarily connected with generalization in ab- 
straction ; generalization is indeed dependent 
on abstraction, which it supposes; but ab- 
straction does not involve generalization.'' 

II. Generalization^ by which is meant the 
process of forming Concepts or General Idea. 
It acts in the direction of apprehending the 
common qualities of objects, persons and 
things, and combining and imiting them into 
a single notion or conception which will com- 
prehend and include them all. A General 
Idea or Concept differs from a particular idea 
in that it includes within itself the qualities of 
the particular and other particulars, and ac- 
cordingly may be applied to any one of these 



Process of Eeasoning 19 

particulars as well as to the general class. For 
instance, one may have a particular idea of 
some particular horse, which applies only to 
that particular horse. He may also have a 
General Idea of horse, in the generic or class 
sense, which idea applies not only to the gen- 
eral class of horse but also to each and every 
horse which is included in that class. The ex- 
pression of Generalization or Conception is 
called a Concept. 

III. Judgment, by which is meant the proc- 
ess of comparing two objects, persons or 
things, one with another, and thus perceiving 
their agreement or disagreement. Thus we 
may compare the two concepts horse and ani- 
mal, and perceiving a certain agreement be- 
tween them we form the judgment that: *^A 
horse is an animal ;^^ or comparing horse and 
cow, and perceiving their disagreement, we 
form the judgment: ^^A horse is not a cow/^ 
The expression of a judgment is called a 
Proposition. 

IV. Reasoning, by which is meant the 
process of comparing two objects, persons or 
things, through their relation to a third object, 
person or thing. Thus we may reason (a) 



20 Logical Thinking 

thai all mammals are animals; (b) that a 
horse is a mammal; (c) that, therefore^ a 
horse is an animal ; the result of the reasoning 
being the statement that: ^^A horse is an 
animal. ' ' The most fundamental principle of 
reasoning, therefore, consists in the compar- 
ing of two objects of thought through and by 
means of their relation to a third object. The 
natural form, of expression of this process of 
Reasoning is called a Syllogism. 

It will be seen that these four processes of 
reasoning necessitate the employment of the 
processes of Analysis and Synthesis, respect- 
ively. Analysis means a separating of an 
object of thought into its constituent parts, 
qualities or relations. Synthesis means the 
combining of the qualities, parts or relations 
of an object of thought into a composite whole. 
These two processes are found in all processes 
of Eeasoning. Abstraction is principally 
analytic ; 6'eneralization or Conception chiefly 
synthetic; Judgment is either or both analytic 
or synthetic ; Eeasoning is *^ either a synthesis 
of particulars in Induction, or an evolution 
of the particular from the general in Deduc- 
tion. 



Process of Reasoning 21 

There are two great classes of Reasoning; 
viz., (1) Inductive Reasoning, or the infer- 
ence of general truths from particular truths ; 
and (2) Deductive Reasoning, or the infer- 
ence of particular truths from general truths. 

Inductive Reasoning proceeds by discover- 
ing a general truth from particular truths. 
For instance, from the particular truths that 
individual men die we discover the general 
truth that **A11 men must die;'' or from ob- 
serving that in all observed instances ice 
melts at a certain temperature, we may infer 
that ** All ice melts at a certain temperature.'' 
Inductive Reasoning proceeds from the 
known to the unknown. It is essentially a 
synthetic process. It seeks to discover gen- 
eral laws from particular facts. 

Deductive Reasoning proceeds by discover- 
ing particular truths from general truths. 
Thus we reason that as all men die, John 
Smith, being a man, must die ; or, that as all 
ice melts at a certain temperature, it f oUows 
that the particular piece of ice under consid- 
eration will melt at that certain temperature. 
Deductive Reasoning is therefore seen to be 
essentially an analytical process. 



22 Logical Thinking 

Mills says of Inductive Eeasoning: ^^The 
inductive method of the ancients consisted in 
ascribing the character of general truths to all 
propositions which are true in all the instances 
of which we have knowledge. Bacon exposed 
the insufficiency of this method, and physical 
investigation has now far outgrown the Ba- 
conian conception. . . . Induction, then, 
is that operation by which we infer that what 
we know to be true in a particular case or 
cases, will be true in all cases which resemble 
the former in certain assignable respects. In 
other words, induction is the process by which 
we conclude that what is true of certain in- 
dividuals of a class is true of the whole class, 
or that what is true at certain times will be 
true in similar circumstances at all times. '^ 

Eegarding Deductive Eeasoning, a writer 
says: *^ Deductive Eeasoning is that process 
of reasoning by which we arrive at the neces- 
sary consequences, starting from admitted or 
established premises.^ ^ Brooks says: **The 
general truths from which we reason to par- 
ticulars are derived from several distinct 
sources. Some are intuitive, as the axioms 
of mathematics or logic. Some of them are 



Pkocess of Reasoning 23 

derived from induction. . . . Some of 
them are merely hypothetical, as in the in- 
vestigation of the physical sciences. Many of 
the hypotheses and theories of the physical 
sciences are used as general truth for de- 
ductive reasoning; as the theory of gravita- 
tion, the theory of light ; etc. Eeasoning from 
the theory of universal gravitation, Leverrier 
discovered the position of a new planet in the 
heavens before it had been discovered by 
human eyes.'' 

Halleck points out the interdependence of 
Inductive and Deductive Eeasoning in the 
following words: ^*Man has to find out 
through his own experience, or that of others, 
the major premises from which he argues or 
draws his conclusions. By induction we ex- 
amine what seems to us a sufficient number of 
individual cases. We then conclude that the 
rest of these cases, which we have not exam- 
ined, will obey the same general laws. . . . 
The premise, ^ All cows chew the cud,' was laid 
down after a certain nrnnber of cows had been 
examined. If we were to see a cow twenty 
years hence, we should expect that she chewed 
her cud. . . . After Induction has classi- 



24 LoGiCAii Thinking 

fied certain phenomena and tlvus given us a 
major premise, we proceed deductively to ap- 
ply the inference to any new specimen that 
can be shown to belong to that class.'' 

The several steps of Deductive Eeasoning 
shall now be considered in turn as we proceed. 



CHAPTER III. 

THE CONCEPT 

In considering the process of thinking, we 
must classify the several steps or stages of 
thought that we may examine each in detail 
for the purpose of comprehending them com- 
bined as a whole. In actual thinking these 
several steps or stages are not clearly sep- 
arated in consciousness, so that each stands 
out clear and distinct from the preceding and 
succeeding steps or stages, but, on the con- 
trary, they blend and shade into each other 
so that it is often difficult to draw a clear di- 
viding line. The first step or stage in the 
process of thinking is that which is called 
a concept. 

A concept is a mental representation of 
anything. Prof. Wm. James says: ^^The 
function by which we mark off, discriminate, 
draw a line around, and identify a numerically 
distinct subject of discourse is called concep- 
tion.^^ There are five stages or steps in each 
concept, as follows : 

25 



26 Logical. Thinking 

I. Presentation. Before a concept may be 
formed there must first be a presentation of 
the material from which the concept is to be 
formed. If we wish to form the concept, 
animaly we must first have perceived an ani- 
mal, probably several kinds of animals— 
horses, dogs, cats, cows, pigs, lions, tigers, 
etc. We must also have received impressions 
from the sight of these animals which may be 
reproduced by the memory— represented to 
the mind. In order that we may have a full 
concept of animal we should have perceived 
every kind of animal, for otherwise there 
would be some elements of the full concept 
lacking. Accordingly it is practically impossi- 
ble to have a full concept of anything. The 
greater the opportunities for perception the 
greater will be the opportunity for concep- 
tion. In other books of this series we have 
spoken of the value and importance of the at- 
tention and of clear and full perception. With- 
out an active employment of the attention, it 
is impossible to receive a clear perception of 
anything; and unless the perception has been 
clear, it is impossible for the mind to form a 
clear concept of the thing perceived. As Sir 



The Concept 27 

Wm. Hamilton has said: ^^An act of atten- 
tion, tliat is an act of concentration, seems 
thus necessary to every exertion of conscious- 
ness, as a certain contraction of the pupil is 
requisite to every exertion of vision. • . . 
Attention, then, is to consciousness what the 
contraction of the pupil is to sight, or to the 
eye of the mind what the microscope or tele- 
scope is to the bodily eye. ... It consti- 
tutes the half of all intellectual power. ' ' And 
Sir B. Brodie said: ^^It is attention, much 
more than in the abstract power of reasoning, 
which constitutes the vast difference which 
exists between minds of different individ- 
uals. ' ' And as Dr. Beattie says : ^ * The force 
with which anything strikes the mind is gen- 
erally in proportion to the degree of attention 
bestowed upon it. ^ ' 

II. Comparison. Following the stage of 
Presentation is the stage of Comparison. We 
separate our general concept of animal into 
a number of sub-concepts, or concepts of var- 
ious kinds of animals. We compare the pig 
with the goat, the cow with the horse, in fact 
each animal with all other animals known to 
us. By this process we distinguish the points 



28 Logical Thinking 

of resemblance and the points of difference. 
We perceive that the wolf resembles the dog 
to a considerable degree; that it has some 
points of resemblance to the fox; and a still 
less distinct resemblance to the bear; also 
that it differs materially from the horse, the 
cow or the elephant. We also learn that there 
are various kinds of wolves, all bearing a 
great resemblance to each other, and yet hav- 
ing marked points of difference. The closer 
we observe the various individuals among the 
wolves, the more points of difference do we 
find. The faculty of Comparison evidences 
itself in inductive reasoning; ability and dis- 
position to analyze, classify, compare, etc. 
Fowler says that those in whom it is largely 
developed ^^Eeason clearly and correctly from 
conclusions and scientific facts up to the laws 
which govern them ; discern the known from 
the unknown; detect error by its incongruity 
with facts ; have an excellent talent for com- 
paring, explaining, expounding, criticising, 
exposing, etc.'' Prof. William James says: 
**Any personal or practical interest in the 
results to be obtained by distinguishing, 
makes one's wits amazingly sharp to detect 



The Concept 29 

differences. And long training and practice 
in distinguishing has the same effect as per- 
sonal interest. Bioth of these agencies give 
to small amounts of objective difference the 
same effectiveness upon the mind that, under 
other circumstances, only large ones would 
make.'' 

in. Abstraction. Following the stage of 
Comparison is that of Abstraction. The term 
^^Abstraction'' as used in psychology means: 
^^The act or process of separating from the 
numerous qualities inherent in any object, the 
particular one which we wish to make the sub- 
ject of observation and reflection. Or, the act 
of withdrawing the consciousness from a num- 
ber of objects with a view to concentrate it on 
some particular one. The negative act of 
which Attention is the positive. ' ' To abstract 
is ^ ^ to separate or set apart. ' ' In the process 
of Abstraction in our consideration of ani- 
malsy after having recognized the various 
points of difference and resemblance between 
the various species and individuals, we pro- 
ceed to consider some special quality of ani- 
mals, and, in doing so, we abstract^ set aside, 
or separate the particular quality which we 



30 Logical Thinking 

wish to consider. If we wish to consider the 
size of animals, we abstract the quality of 
size from the other qualities, and consider 
animals with reference to size alone. Thus 
we consider the various degrees of size of the 
various animals, classifying them accord- 
ingly. In the same way we may abstract the 
quality of shape, color or habits, respectively, 
setting aside this quality for special observa- 
tion and classification. If we wish to study, 
examine or consider certain qualities in a thing 
we abstract that particular quality from the 
other qualities of the thing; or we abstract 
the other qualities until nothing is left but the 
particular quality under consideration. In 
examining or considering a class or num- 
ber of things, we first abstract the qualities 
possessed in common by the class or number 
of things; and also al)stract or set aside the 
qualities not comnwn to them. 

For instance ; in considering classes of ani- 
mals, we abstract the combined quality of 
milk-giving and pouch-possessing which is 
possessed in common by a number of animals ; 
then we group these several animals in a class 
which we name the Marsupialiaj of which the 



The Concept 31 

opossum and kangaroo are members. In 
these animals the young are brought forth in 
an imperfect condition, undeveloped in size 
and condition, and are then kept in the pouch 
and nourished until they are able to care for 
themselves. Likewise, we may abstract the 
idea of the placenta^ the appendage which 
connects the young unborn animal with the 
mother, and by means of which the foetus is 
nourished. The animals distinguished by this 
quality are grouped together as the Placental 
Mammals. The Placental Mammals are di- 
vided into various groups, by an Abstraction 
of qualities or class resemblance or difference, 
as follows: The Edentata, or toothless 
creatures, such as the sloths, ant-eaters, arm- 
adillos, etc. ; the Sirenia, so-named from their 
fancied resemblance to the fabled^* sirens,'^ 
among which class are the sea-cows, manatees, 
dugongs, etc.; the Cetacea, or whale family, 
which although fish-like in appearance, are 
really mammals, giving birth to living young 
which they nourish with breast-milk, among 
which are the whales, porpoises, dolphins, 
etc.; the Ungulata, or hoofed animals, such 
as the horse, the tapir, the rhinoceros, the 



32 Logical Thinking 

swine, the hippopotamus, the camel, the deer, 
the sheep, the cow, etc. ; the Eyracoidea, hav- 
ing teeth resembling both the hoofed animals 
and the gnawing animals, of which the coney 
or rock-rabbit is the principal example; the 
Proboscidea, or trunked animals, which fam- 
ily is represented by the various families of 
elephants; the Carnivora, or flesh-eaters, 
represented by various sub-families and 
species ; the Rodentia, or gnawers ; the Insect- 
ivora, or insect feeders; the Cheiroptera, or 
finger-winged; the Lemuroidea, or lemurs, 
having the general appearance of the monkey, 
but also the long bushy tail of the fox; the 
Primates^ including the monkeys, baboons, 
man-apes, gibbons, gorillas, chimpanzees, 
orang-outangs and Man. 

In all of these cases you will see that each 
class or general family possesses a certain 
common quality\^]\\Qh. gives it its classifica- 
tion, and which quality is the subject of the 
Abstraction in considering the particular 
group of animals. Further and closer Ab- 
straction divides these classes into sub- 
classes; for instance, the family or class of 
the Carnivora, or flesh-eaters, may be di- 



The Concept 33 

vided by further Abstraction into the classes 
of seals, bears, weasels, wolves, dogs, lions, 
tigers, leopards, etc. In this process, we must 
first make the more general Abstraction of 
the wolf and similar animals into the dog- 
family; and the lion, tiger and similar forms 
into the cat-family. 

Halleck says of Abstraction : ^ ^ In the proc- 
ess of Abstraction, we draw our attention 
away from a mass of confusing details, unim- 
portant at the time, and attend only to quali- 
ties common to the class. Abstraction is little 
else than centering the power of attention on 
some qualities to the exclusion of others. '' 

IV. Generalization. Arising from the 
stage of Abstraction is the stage of General- 
ization. Generalization is : ^ ' The act or proc- 
ess of generalizing or making general ; bring- 
ing several objects agreeing in some point 
under a common or general name, head or 
class ; an extending from particulars to gen- 
erals; reducing or arranging in a genus; 
bringing a particular fact or series of facts 
into a relation with a wider circle of facts.'' 
As Bolingbroke says: *^The mind, therefore, 
makes its utmost endeavors to generalize its 



34 Logical Thinking 

ideas, beginning early with such as are most 
familiar and coming in time to those which are 
less so.'* Under the head of Abstraction we 
have seen that through Abstraction we may 
Generalize the various species into the var- 
ious families, and thus, in turn, into the vari- 
ous sub-families. Following the same process 
we may narrow down the sub-families into 
species composed of various individuals; or 
into greater and still greater families or 
groups. Generalization is really the act of 
Classification, or forming into classes all 
things having certain qualities or properties 
in common. The corollary is that all things 
in a certain generalized class must possess the 
particular quality or property common to the 
class. Thus we know that all animals in the 
class of the Carnivora must eat flesh ; and that 
all Mammals possess breasts from which they 
feed their young. As Halleck says: ^*We 
put all objects having like qualities into a cer- 
tain genus, or class. When the objects are in 
that class, we know that certain qualities will 
have a general application to them alV^ 

V. Denomination. Following closely upon 
the step of Generalization or Classification, 



The Concept 35 

is the step of Denomination. By Denomina- 
tion we mean ^Hhe act of naming or designat- 
ing by a name.'' A name is the symbol by 
which we think of a familiar thing without the 
necessity for making a distinct mental image 
upon each occasion of thought. Or, it may be 
considered as akin to a label affixed to a thing. 
As in the case of the algebraic symbols, a, b, c, 
X, and 2/, by the use of which we are able to 
make intricate calculations easily and rapidly, 
so may we use these word symbols much more 
readily than we could the lengthy descriptions 
or even the mental images of the thing sym- 
bolized. It is much easier for us to think 
''horse^^ than it would be to think the full 
definition of that animal, or to think of it by 
recalling a mental picture of the horse each 
time we wished to think of it. Or, it is much 
better for us to be able to glance at a label on 
a package or bottle than to examine the con- 
tents in detail. As Hobbes says: *^A word 
taken at pleasure to serve for a mark, which 
may raise in our minds a thought like to some 
thought we had before, and which being pro- 
nounced to others, may be to them a sign of 
what thought the speaker had or had not. 



36 Logical Thinking 

before in his mind.'' Mill says: **A name 
is a word (or set of words) serving the 
double purpose of a mark to recall to our- 
selves the likeness of a former thought and as 
a sign to make it known to others." Some 
philosophers regard names as symbols of our 
ideas of things, rather than of the things 
themselves; others regard them as symbols 
of the things themselves. It will be seen that 
the value of a name depends materially upon 
the correct meaning and understanding re- 
garding it possessed by the person using it. 



CHAPTER IV. 

THE USE OF CONCEPTS 

Having observed the several steps or stages 
of a concept, let ns now consider the use and 
misuse of the latter. At first glance it would 
appear difficult to misuse a concept, but a little 
consideration will show that people very com- 
monly fall into error regarding their concepts. 

For instance, a child perceives a horse, a 
cow or a sheep and hears its elders apply the 
term ^'ammaV^ to it. This term is perfectly 
correct, although symbolizing only a very gen- 
eral classification or generalization. But, the 
child knowing nothing of the more limited and 
detailed classification begins to generalize re- 
garding the animal. To it, accordingly, an 
' * animal" is identical with the dog or the cow, 
the sheep or the horse, as the case may be, and 
when the term is used the child thinks that 
all animals are similar to the particular an- 
imal seen. Later on, when it hears the term 
** animal '^ applied to a totally different look- 
ing creature, it thinks that a mistake has been 

37 



38 Logical Thinking 

made and a state of confusion occurs. Or, 
even when a term is applied within narrower 
limits, the same trouble occurs. The child 
may hear the term ^ * dog' ^ applied to a mastiff, 
and it accordingly forms a concept of dog 
identical with the qualities and attributes of 
the mastiff. Later, hearing the same term 
applied to a toy-terrier, it becomes indignant 
and cries out that the latter is no ^^dog" but 
is something entirely different. It is not until 
the child becomes acquainted with the fact 
that there are many kinds of creatures in the 
general category of ^^dog'' that the latter 
term becomes fully understood and its ap- 
propriate concept is intelligently formed. 
Thus we see the importance of the step of Pre- 
sentation. 

In the same way the child might imagine 
that because some particular ^^man^' had red 
hair and long whiskers, all men were red- 
haired and long-whiskered. Such a child 
would always form the concept of **man'' as a 
creature possessed of the personal qualities 
just mentioned. As a writer once said, read- 
ers of current French literature might imag- 
ine that all Englishmen were short, dumpy, 



Use of Coitcepts 39 

red-cheeked and irascible, and that all Eng- 
lishwomen had great teeth and enormous feet ; 
also that readers of English literature might 
imagine that all Frenchmen were like mon- 
keys, and all Frenchwomen were sad co- 
quettes. In the same way many American 
young people believe that all Englishmen say 
^* Don't you know" and all Englishwomen 
constantly ejaculate: ** Fancy!'* Also that 
every Englishman wears a monocle. In the 
same way, the young English person, from 
reading the cheap novels of his own country, 
might well form the concept of all Americans 
as long-legged, chin-whiskered and big-nosed, 
saying ' ' Waal, I want to know ; " ^ ^ I reckon ; ' ' 
and ^^Du tell;" while they tilted themselves 
back in a chair with their feet on the mantel- 
piece. The concept of a Western man, enter- 
tained by the average Eastern person who has 
never traveled further West than Buffalo, is 
equally amusing. In the same way, we have 
known Western people who formed a concept 
of Boston people as partaking of a steady and 
continuous diet of baked beans and studiously 
reading Browning and Emerson between 
these meals. 



40 Logical Thinking 

Halleck says : *^ A certain Norwegian child 
ten years old had the quality white firmly im- 
bedded in his concept man. Happening one 
day to see a negro for the first time, the child 
refused to call him a man until the negro's 
other qualities compelled the child to revise 
his concept and to eliminate whiteness. If 
that child should ever see an Indian or a 
Chinaman, the concept would undergo still 
further revision. A girl of six, reared with 
an intemperate father and brothers, had the 
quality of drunkenness firmly fixed in her con- 
cept of man. A certain boy kept, until the 
age of eleven, trustworthiness in his concept 
of man. Another boy, until late in his teens 
thought that man was a creature who did 
wrong not from determination but from ignor- 
ance, that any man would change his course 
to the right path if he could but understand 
that he was going wrong. Happening one 
day to hear of a wealthy man who was neglect- 
ing to provide comforts for his aged mother 
in her last sickness, the boy concluded that 
the man did not know his mother's condition. 
When he informed the man, the boy was told 
to mind his own business. The same day he 



Use of Concepts 41 

heard of some politicians who had intention- 
ally cheated the city in letting a contract and 
he immediately revised his concept. It must 
be borne in mind that most of our concepts 
are subject to change during our entire life; 
that at first they are made only in a tentative 
way; that experience may show us, at any 
time, that they have been erroneously formed, 
that we have, abstracted too little or too much, 
made this class too wide or too narrow, or that 
here a quality must be added or there one 
taken away/' 

Let us now consider the mental processes 
involved in the formation and use of a con- 
cept. We have first, as we have seen, the 
presentation of the crude material from which 
the concept must be formed. Our attention 
being attracted to or directed toward an ob- 
ject, we notice its qualities and properties. 
Then we begin a process of comparison of the 
object perceived or of our perception of it. 
We compare the object with other objects or 
ideas in our mind, noting similarities and dif- 
ferences and thereby leading towards classifi- 
cation with similar objects and opposed dis- 
similar ones. The greater the range of other 



42 Logical Thinking 

objects previously perceived, the greater will 
be the number of relations established between 
the new object or idea and others. As we ad- 
vance in experience and knowledge, the web 
of related objects and ideas becomes more 
intricate and complex. The relations attach- 
ing to the child's concept of horse is very 
much simpler than the concept of the experi- 
enced adult. Then we pass on to the step of 
analysis, in which we separate the qualities of 
the object and consider them in detail. The 
act of abstraction is an analytical process. 
Then we pass on to the step of synthesis, in 
which we unite the materials gathered by 
comparison and analysis, and thus form a 
general idea or concept regarding the object. 
In this process we combine the various quali- 
ties discerned by comparison and analysis, 
and grouping them together as in a bundle, we 
tie them together with the string of synthesis 
and thus have a true general conception. Thus 
from the first general conception of horse as 
a simple thing, we notice first that the animal 
has certain qualities lacking in other things 
and certain others similar to other things; 
then we analyze the various qualities of the 



Use of Concepts 43 

horse, recognized through comparison, until 
we have a clear and distinct idea of the vari- 
ous parts, qualities and properties of the 
horse; then we synthesize, and joining to- 
gether these various conceptions of the said 
qualities, we at last form a clear general con- 
cept of the horse as he is, with all his qualities. 
Of course, if we later discover other qualities 
attached to the horse, we add these to our gen- 
eral synthesized concept— our concept of 
horse is enlarged. 

Of course these various steps in the forma- 
tion and use of a concept are not realized as 
distinct acts in the consciousness, for the proc- 
esses are largely instinctive and subcon- 
scious, particularly in the case of the ex- 
perienced individual. The subconscious, or 
habit mind, usually attends to these details 
for us, except in instances in which we deliber- 
ately apply the will to the task, as in cases of 
close study, in which we take the process from 
the region of the involuntary and place it in 
the voluntary category. So closely related 
and blended are these various steps of the 
process, that some authorities have disputed 
vigorously upon the question as to which of 



44 Logical Thinking 

the two steps, comparison or analysis, pre- 
cedes the other. Some have claimed that an- 
alysis must precede comparison, else how 
could one compare without having first anal- 
yzed the things to be compared. Others 
hold that comparison must precede analysis, 
else how conld one note a quality xmless he 
had his attention drawn to it by its resem- 
blance to or difference from qualities in other 
objects. The truth seems to lie between the 
two ideas, for in some cases there seems to 
be a perception of some similarity or differ- 
ence before any analysis or abstraction takes 
place; while in others there seems to be an 
analysis or abstraction before comparison is 
possible. In this book we have followed the 
arrangement favored by the latest authori- 
ties, but the question is still an open one to 
many minds. 

As we have seen, the general concept once 
having been formed, the mind proceeds to 
classify the concept with others having gen- 
eral qualities in common. And, likewise, it 
proceeds to generalize from the classification, 
assuming certain qualities in certain classes. 
Then we proceed to make still further general- 



Use of Concepts 45 

izations and classifications on an ascending 
and widening scale, including seeming resem- 
blances less marked, until finally we embrace 
the object with other objects in as large a 
class as possible as well as in as close and 
limited a sub-class as possible. As Brooks 
says: *' Generalization is an ascending proc- 
ess. The broader concept is regarded as 
higher than the narrower concept ; a concept 
is considered higher than a percept ; a general 
idea stands above a particular idea. We thus 
go up from particulars to generals ; from per- 
cepts to concepts; from lower concepts to 
higher concepts. Beginning down with par- 
ticular objects, we rise from them to the gen- 
eral idea of their class. Having formed a 
number of lower classes, we compare them as 
we did individuals and generalize them into 
higher classes. We perform the same proc- 
ess with these higher classes, and thus pro- 
ceed until we are at last arrested in the high- 
est class. Being. Having reached the pinna- 
cle of generalization, we may descend the 
ladder by reversing the process through which 
we ascend.^' 

From this process of generalization, or syn- 



46 Logical Thinking 

thesis, we create from our simple concepts 
our general concepts. Some of the older au- 
thorities distinguished between these two 
classes by terming the former ^^conceptions," 
and reserving the term ^^ concepts '* for the 
general concepts. Brooks says of this : * ' The 
products of generalization are general ideas 
called concepts. We have already discussed 
the method of forming conceptions and now 
consider the nature of the concept itself. 
. . . A concept is a general idea. It is a 
general notion which has in it all that is com- 
mon to its own class. It is a general scheme 
which embraces all the individuals of the 
class while it resembles in all respects none 
of its class. Thus my conception of a quad- 
ruped has in it all four-footed animals, but it 
does not correspond in all respects to any par- 
ticular animals; my conception of a triangle 
embraces all triangles, but does not agree in 
details with any particular triangle. The 
general conception cannot be made to fit ex- 
actly any particular object, but it teems with 
many particulars. These points may be il- 
lustrated with the concepts horse, bird, color, 
animal, etc.'* 



Use of Concepts 47 

So we may begin to perceive tbe distinction 
and difference between a concept and a mental 
image. This distinction, and the fact that a 
concept cannot be imaged j is generally diffi- 
cult for the beginner. It is important that 
one should have a clear and distinct under- 
standing regarding this point, and so we shall 
consider it further in the following chapter. 



CHAPTEE V. 

CONCEPTS AND IMAGES 

As we have said, a concept cannot be im- 
aged—cannot be used as the subject of a 
mental image. This statement is perplexing 
to the student who has been accustomed to the 
idea that every conception of the mind is cap- 
able of being reproduced in the form of a men- 
tal image. But the apparently paradoxical 
statement is seen as quite simple when a little 
consideration is given to it. 

For instance, you have a distinct general 
concept of animal. You know what you mean 
when you say or think, animal. You recog- 
nize an animal when you see one and you un- 
derstand what is meant when another uses 
the word in conversation. But you cannot 
form a meipital image of the concept, animal. 
Why? Because any mental image you might 
form would be either a picture of some par- 
ticular animal or else a composite of the quali- 
ties of several animals. Your concept is too 
broad and general to allow of a composite 

48 



Concepts and Images 49 

picture of all animals. And, in truth, your 
concept is not a picture of anything that actu- 
ally exists in one particular, but an abstract 
idea embracing the qualities of all animals. 
It is like the algebraic x—a symbol for some- 
thing that exists, but not the thing itself. 

As Brooks says: ^^ A concept cannot be rep- 
resented by a concrete image. This is evi- 
dent from its being general rather than parti- 
cular. If its color, size or shape is fixed by an 
image, it is no longer general but particular. ' ' 
And Halleck says: '^It is impossible to image 
anything without giving that image individual 
marks. The best mental images are so defi- 
nite that a picture could be painted from them. 
A being might come under the class man and 
have a snub nose, blonde hair, scanty eye- 
brows, and no scar on his face. The presence 
of one of these individual peculiarities in the 
concept man would destroy it. If we form 
an image of an apple, it must be either of a 
yellow, red, green, or russet apple, either as 
large as a pippin or as small as a crab-apple. 
A boy was asked what he thought of when 
^apple^ was mentioned. He replied that he 
thought of ' a big, dark-red, apple with a bad 



50 Logical Thinking 

spot on one side, near the top.' That boy 
could image distinctly, but his power of form- 
ing concepts was still in its infancy. ' ' 

So we see that while a mental image must 
picture the particular and individual quali- 
ties, properties and appearances of some par- 
ticular unit of a class, a concept can and must 
contain only the class qualities— thai is, the 
qualities belonging to the entire class. The 
general concept is as has been said *^a general 
idea ... a general notion which has in 
it all that is common to its own class. ' ' And 
it follows that a '^ general idea'' of this kind 
cannot be pictured. A picture must be of 
some particular thing, while a concept is 
something above and higher than particular 
things. We may picture a man^ but we cannot 
picture Man the concept of the race. A con- 
cept is not a reproduction of the image of a 
thing^ but on the contrary is an idea of a class 
of things. We trust that the student will con- 
sider this point until he arrives at a clear un- 
derstanding of the distinction, and the reason 
thereof. 

But, while a concept is incapable of being 
pictured mentally as an image, it is true that 



Concepts and Images 51 

some particular representative of a class may 
be held in the mind or imagination as an ideal- 
ized object, as a general representative of the 
class, when we speak or think of the general 
term or concept, providing that its real rela- 
tion to the concept is recognized. These ideal- 
ized objects, however, are not concepts— they 
are percepts reproduced by the memory. It is 
important, however, to all who wish to convey 
their thought plainly, that they be able to 
convert their concepts into idealized repre- 
sentative objects. Otherwise, they tend to be- 
come too idealistic and abstract for common 
comprehension. As Halleck well says: *^We 
should in all cases be ready to translate our 
concepts, when occasion requires, into the 
images of those individuals which the concept 
represents. A concept means nothing except 
in reference to certain individuals. Without 
them it could never have had existence and 
they are entitled to representation. A man 
who cannot translate his concepts into defi- 
nite images of the proper objects, is fitted 
neither to teach, preach, nor practice any pro- 
fession. . . . There was, not long ago, a 
man very fond of talking about fruit in the ab- 



52 Logical Thinking 

stract ; but he failed to recognize an individual 
cranberry when it was placed before him. A 
humorist remarked that a certain metaphysi- 
cian had such a love for abstractions, and such 
an intense dislike for concrete things, as to 
refuse to eat a concrete peach when placed be- 
fore him." 

In the beginning many students are per- 
plexed regarding the difference between a 
percept and a concept. The distinction is sim- 
ple when properly considered. A percept is : 
* ^ the object of an act of perception ; that which 
is perceived. ' ' A concept is : ^ ^ a mental rep- 
resentation." Brooks makes the following 
distinction : ^ ' A percept is the mental product 
of a real thing; a concept is a mere idea or no- 
tion of the common attributes of things. A 
percept represents some particular object; a 
concept is not particular, but general. A per- 
cept can be described by particulars; a con- 
cept can be described only by generals. The 
former can usually be represented by an im- 
age , the latter cannot be imagined, it can only 
he thought.^ ^ Thus one is able to image the 
percept of a particular horse which has been 
perceived; but he is unable to image correctly 



Concepts and Images 53 

tlie concept of horse as a class or generic term. 
In connection with this distinction between 
perception and conception, we may as well 
consider the subject of apperception, a term 
favored by many modern psychologists, al- 
though others steadfastly decline to recognize 
its necessity or meaning and refuse to employ 
it. Apperception may be defined as: ^^per- 
ception accompanied by comprehension ; per- 
ception accompanied by recognition." The 
thing perceived is held to be comprehended or 
recognized— that is, perceived in a new sense, 
by reason of certain previously acquired ideas 
in the mind. Halleck explains it as: ^Hhe 
perception of things in relation to the ideas 
which we already possess.'^ It follows that 
all individuals possessed of equally active or- 
gans of perception, and equally actit^e atten- 
tion, will perceive the same thing in the same 
way and in the same degree. But the apper- 
ception of each individual will differ and vary 
according to his previous experience and 
training, temperament and taste, habit and 
custom. For instance, the familiar story of the 
boy who climbed a tree and watched the 
passers-by, noting their comments. The first 



54 Logical Thinking 

passer-by noticing the tree, says aloud : ' ' That 
would make a good stick of timber/* ^^Good 
morning, Mr. Carpenter,*' said the boy. The 
next man said: *^That tree has fine bark.'* 
^^Good morning, Mr. Tanner,'* said the boy. 
Another said, ^^I bet there's a squirrel *s nest 
up in that tree.** *^Good morning, Mr. 
Hunter, * ' said the boy. 

The woman sees in a bird something pretty 
and ^^ cunning.*' The hunter sees in it some- 
thing to kill. The ornithologist sees it as 
something of a certain genus and species, and 
perhaps also as something appropriate for his 
collection. The farmer perceives it to be 
something destructive of either insects or 
crops. A thief sees a jail as something to be 
dreaded ; an ordinary citizen, something use- 
ful for confining objectionable people; a po- 
liceman, something in the line of his busi- 
ness. And so on, the apperception differing 
upon the previous experience of the indi- 
vidual. In the same way the scientist sees in 
an animal or rock many qualities of which the 
ordinary person is ignorant. Our training, 
experience, prejudices, etc., affect our apper- 
ception. 



Concepts and Images 55 

And so, we see that in a measure our con- 
cepts are determined not only by our simple 
perceptions, but also materially by our apper- 
ceptions. We conceive things not only as they 
are apparent to our senses, but also as colored 
and influenced by our previous impressions 
and ideas. For this reason we find widely 
varying concepts of the same things among 
different individuals. Only an absolute ndnd 
could form an absolute concept. 



CHAPTER VI. 

TERMS 

In logic the words concept and term are 
practically identical, but in the popular usage 
of the terms there is a distinct difference. This 
difference is warranted, if we depart from the 
theoretical phase of logic, for the word con- 
cept really denotes an idea in the mind, while 
the word term really denotes a word or name 
of an idea or concept— the symbol of the latter. 
In a previous chapter we have seen that De- 
nomination, or ^ ' the act of naming or designat- 
ing by a name'' is the final step or stage in 
forming a concept. And it is a fact that the 
majority of the words in the languages of 
civilized people denote general ideas or con- 
cepts. As Brooks says : ^ ^ To give each indi- 
vidual or particular idea a name peculiar to it- 
self would be impracticable and indeed impos- 
sible; the mind would soon become over- 
whelmed with its burden of names. Nearly all 
the ordinary words of our language are gen- 
eral rather than particular. The individuals 

56 



Tebms 57 

distinguished by particular names, excepting 
persons and places, are comparatively few. 
Most objects are named only by common 
nouns ; nearly all of our verbs express general 
actions ; our adjectives denote common quali- 
ties, and our adverbs designate classes of ac- 
tions and qualities. There are very few words 
in the language, besides the names of persons 
and places, that do not express general ideas. ' ' 
In logic the word term is employed to denote 
any word or words which constitute a concept. 
The word concept is employed strictly in the 
sense of a subject of thought, without refer- 
ence to the words symbolizing it. The con'- 
cept, or subject of thought, is the important 
element or fact and the term denoting it is 
merely a convenient symbol of expression. It 
must be remembered that a term does not 
necessarily consists of but a single word, for 
often many words are employed to denote the 
concept, sometimes even an entire clause or 
phrase being found necessary for the current 
term. For the purpose of the consideration 
of the subjects to be treated upon in this book, 
we may agree that: A term is the outward 



58 Logical Thinkii^g 

symbol of a concept; and that: The concept 
is the idea expressed by the term. 

There are three general parts or phases of 
Deductive Logic, namely: Terms, Proposi- 
tions and Syllogisms. Therefore, in consider- 
ing Terms we are entering into a considera- 
tion of the first phase of Deductive Logic. Un- 
less we have a correct understanding of 
Terms, we cannot expect to understand the 
succeeding stages of Deductive Eeasoning. 
As Jevons says: *^When we join terms to- 
gether we make a Proposition; when we join 
Propositions together, we make an argument 
or piece of reasoning. . . . We should 
generally get nothing but nonsense if we were 
to put together any terms and any proposi- 
tions and to suppose that we were reasoning. 
To produce a good argument we must be care- 
ful to obey certain rules, which it is the pur- 
pose of Logic to make known. But, in order to 
understand the matter perfectly, we ought 
first to learn exactly what a term is, and how 
many hinds of terms there may be; we have 
next to learn the nature of a proposition and 
the different kinds of propositions. After- 
wards we shall learn how one proposition may 



Terms 59 

by reasoning be drawn from other proposi- 
tions in the kind of argument called the 
syllogism.'^ 

Now, having seen that terms are the out- 
ward symbols or expression of concepts, and 
are the names of things which we join to- 
gether in a proposition, let us proceed to con- 
sider the different kinds of terms, following 
the classifications adopted by the authorities. 

A term may contain any number of nouns, 
substantive or adjective or it may contain but 
a single noun. Thus in, *^ Tigers are fero- 
cious," the first term is the single substantive 
* ^tigers;'' the second term is the single ad- 
jective *^ ferocious." And in the proposition, 
^^The King of England is the Emperor of 
India," there are two terms, each composed 
of two nouns, ^'King of England" being the 
first term and ^* Emperor of India" being the 
second term. The proposition, ^ ' The library 
of the British Museum is the greatest collec- 
tion of books in the world," contains fifteen 
words but only two terms ; the first term being 
**The library of the British Museum," in 
which are two substantives, one adjective, two 
definite articles and one preposition ; the sec- 



60 Logical Thinking 

ond term being, ^41ie greatest collection of 
books in the world, " which contains three sub- 
stantives, one adjective, two articles, and two 
prepositions. The above illustration is sup- 
plied by Jevons, who adds: ^^A logical term, 
then, may consist of any number of nouns, 
substantive or adjective, with the articles, 
prepositions and conjunctions required to join 
them together; still it is only one term if it 
points out, or makes us think of a single ob- 
ject, or collection, or class of objects.^ ^ (A 
substantive, is : ^^the part of speech which ex- 
presses something that e:^sts, either material 

or immaterial. '0 

The first classification of terms divides 
them into two general classes, vi^., (1) Singu- 
lar Terms; and (2) General Terms. 

A Singular Term is a-Mmi denoting a single 
object, person or thing. Although denoting 
only a single object, person or thing, it may 
be composed of several words ; or it may be 
composed of but one word as in the case of a 
proper name, etc. The following are Singular 
Terms, because they are terms denoting but a 
single object, person or thing: *^ Europe ; Min- 
nesota ; Socrates ; Shakespeare ; the first man ; 



Terms 61 

the highest good ; the first cause ; the King of 
England; the British Museum; the Commis- 
sioner of Public Works ; the main street of the 
City of New York." It will be noted that in 
all of the examples given, the Singular Term 
denotes a particular something, a specific 
thing, a something of which there is but one, 
and that one possesses particularity and indi- 
viduality. As Hyslop says : ' ' Oneness of kind 
is not the only or distinctive feature of Singu- 
lar Terms, but individuality, or singularity, as 
representing a concrete individual whole." 

A General Term is a term which applies, in 
the same sense, to each and every individual 
object, person or thing in a number of objects, 
persons or things of the same kind, or to the 
entire class composed of such objects persons 
or things of the same kind. For instance, 
^ ' horse ; man ; biped ; mammal ; trees ; figures ; 
grain of sand ; matter," etc. Hyslop says, re- 
garding General Terms: ^^In these instances 
the terms denote more than one object, and 
apply to all of the same kind. Their meaning 
is important in the interpretation of what are 
called universal propositions." 

Another general classification of Terms di- 



62 Logical Thinking 

vides them into two respective classes, as fol- 
lows: (1) Collective Terms; and (2) Distribu- 
tive Terms. Hyslop says of this classifica- 
tion : ^ ^ This division is based upon the distinc- 
tion between aggregate wholes of the same 
kind and class terms. It partly coincides with 
the division into Singular and General Terms, 
the latter always being distributive.'' 

A Collective Term is one which denotes an 
aggregate or collected whole of objects, per- 
sons or things of the same or similar kind, 
which collective whole is considered as an indi- 
vidual, although composed of a totality of sep- 
arate individual objects, persons or things. 
Thus the following terms: ^^ regiment; con- 
gregation ; army ; family ; crowd ; nation ; com- 
pany ; battalion ; class ; congress ; parliament ; 
convention;" etc. are Collective Terms, be- 
cause they denote collective, aggregate or 
composite wholes, considered as an individual. 

A Distributive Term is a term which denotes 
each and every individual object, person or 
thing in a given class. For example, are the 
terms: *^man; quadruped; biped; mammal; 
book; diamond; tree.'' As Hyslop says: 
^^ General terms are always distributive." 



Teems 63 

Also: ^^It is important also to keep clear the 
distinction between class wholes and collective 
wholes. . . . They are often confused so 
as to call a term denoting a class a Collective 
Term.'* 

Another general classification of Terms 
divides them into the following two respect- 
ive classes; (1) Concrete Terms; and (2) Ab- 
stract Terms. 

A Concrete Term is a term denoting either 
a definite object, person or thing which is sub- 
ject to perception and experience, and may 
be considered as actually existent concretely, 
as for instance: horse; man; mountain; dol- 
lar; knife; table; etc., or else an attribute 
thought of and used solely as an attribute, as 
for instance: *^ beautiful, wise, noble, virtu- 
ous, good,'' etc. 

An Abstract Term is a term denoting the at- 
tribute, quality or property considered as 
apart from the object, person or thing and as 
having an abstract existence, as for instance : 
^^ beauty; wisdom; nobility; goodness; vir- 
tue," etc. As we have seen elsewhere, these 
qualities have no real existence in themselves, 
but are known and thought of only in connec- 



64 Logical Thinking 

tion with concrete objects, persons and things. 
Thus we cannot know ^^ Beauty," but may 
know beautiful things; we cannot know ^^ Vir- 
tue," but we may know virtuous people, etc. 

An attribute or quality is concrete when ex- 
pressed as an adjective; and abstract when 
expressed as a noun; as for instance, ^^beauti- 
ful" and *^ beauty," respectively, or ^^ virtu- 
ous ' ' and ^ ' virtue, ' ' respectively. The distinc- 
tion may be summed up as follows: A Con- 
crete Term is the name of a thing or of a qual- 
ity of a thing expressed as an adjective and as 
merely a quality ; while an Abstract Term is 
the name of a quality of a thing, expressed as 
a noun and as a ^Hhing^^ in itself. 

Certain terms may be used as either Con- 
crete Terms or as Abstract Terms, and cer- 
tain authorities have seen fit to classify them 
as Mixed Terms, as for instance the terms: 
^ ^ government ; religion; philosophy;" etc. 

Another general classification of Terms di- 
vides them into two respective classes as fol- 
lows: (1) Positive Terms; and (2) Negative 
Termis. 

A Positive Term is a term which denotes its 
own qualities, as for instance: ^^good, human. 



Teems 65 

large, square, black, strong," etc. These 
terms indicate the presence of the quality de- 
noted by the term itself. 

A Negative Term is a term denoting the ab- 
sence of a quality, as for instance: ^^ inhuman, 
inorganic, unwell, unpleasant, non-conduc- 
ive, '^ etc. These terms deny the presence of 
certain qualities, rather than asserting the 
presence of an opposite quality. They are es- 
sentially negative in nature and in form. 
Jevons says : ^^ We may usually know a Nega- 
tive Term by its beginning with one of the 
little syllables un-, in-, a-, an-, non-, or by its 
ending with -less. ' ' Hyslop says : ^ ' The usual 
symbols of Negative Terms are in, un, less, 
diSy a, or an, anti, mis, and sometimes de, and 
tiotj and not.'' Jevons adds: ^^If the English 
language were a perfect one, every term ought 
to have a Negative Term exactly correspond- 
ing to it, so that all adjectives and nouns 
would be in pairs. Just as convenient has its 
negative inconvenient; metallic, non-metallic; 
logical, illogical; and so on; so blue should 
have its negative, non-blue; literary, non- 
literary; paper, non-paper. But many of 
these Negative Terms would be seldom or 



66 Logical Thinking 

never used, and if we happen to want them, we 
can make them for the occasion by putting 
not-, or non-, before the Positive Term. Ac- 
cordingly, we find in the dictionary only those 
Negative Terms which are much employed.'* 

The last named authority also says: 
^ ' Sometimes the same word may seem to have 
two or even more distinct negatives. There is 
much difference between undressed and not- 
dressed, that is *not in evening dress.' Both 
seem to be negatives of ^dressed,' but this is 
because the word has two distinct meanings." 

Some authorities insist upon closer and fur- 
ther classification, as for instance, in the case 
of what they call a Privative Term, denoting 
the absence of qualities once possessed by the 
object, person or thing, as : *^deaf, dead, blind, 
dark," etc. Hyslop says that these terms 
^^are Positive in form and Negative in matter 
or meaning." Also in the case of what they 
call a N ego-positive Term, denoting ^Hhe 
presence of a positive quality expressed in a 
negative manner," as : disagreeable, inhuman^ 
invaluable, etc. These last mentioned classes 
however are regarded by some as the result 
of ** carrying too far" the tendency toward 



Terms 67 

classification, and the two general classes, 
Positive and Negative, are thought sufficient 
for the purpose of the general student. The 
same objection applies to a classification oc- 
casionally made i. e., that which is called an 
Infinitated Term, denoting a term the intent 
of which is to place in a distinct category 
every object, person or thing other than that 
expressed in the corresponding Positive 
Term. The intent of the term is to place the 
positive idea in one class, and all else into a 
separate one. Examples of this class of terms 
are found in: ^^not-I, not-animal, not- tree, un- 
moral," etc. Hyslop says of these terms: 
*^They are not always, if ever, recognized as 
rhetorically elegant, but are valuable often to 
make clear the really negative, or infimta- 
tively negative nature of the idea in mind. ' ' 

Another general classification of Terms di- 
vides them into two respective classes, as fol- 
lows: (1) Absolute Terms; and (2) Kelative 
Terms. 

An Absolute Term is a term denoting the 
presence of qualities intrinsic to the object, 
and not depending upon any relation to any 
other object, as for instance: ^^man; book; 



68 Logical THiisrKi:tsrG 

horse; gun;'' etc. These terms may he re- 
lated to many other terms, but are not neces- 
sarily related to any other. 

A Relative Term is a term denoting certain 
necessary relations to other terms, as for in- 
stance: ^'father; son; mother; daughter; 
teacher ; pupil ; master ; servant ; ' ' etc. Thus 
it is impossible to think of ^^ child'' except in 
relation to ^* parent," or vice versa. The one 
term implies the existence of its related term. 

Hyslop says of the above classification: 
^^Kelative Terms suggest the thought of other 
individuals with the relation involved as a 
part of the term's meaning, while Absolute 
Terms suggest only the qualities in the sub- 
ject without a relation to others being neces- 
sarily involved." 

Some authorities also classify terms as 
higher and lower; also as hroad and narrow. 
This classification is meant to indicate the 
content and extent of the term. For instance, 
when we classify, we begin with the individ- 
uals which we then group into a small class. 
These classes we then group into a larger 
class, according to their resemblances. These 
larger classes then go to form a part of still 



Teems 69 

larger classes, and so on. As these classes 
advance they form broader terms; and as we 
retreat from the general class into the less 
general and more particular, the term becomes 
narrower. By some, the broader term which 
includes the narrower is called the higher 
term,, and the narrower are called the lower 
terms. Thus animal would be a higher and 
broader term than dog, cat or tiger because it 
includes the latter. Brooks says: ^^ Since a 
concept is formed by the union of the common 
attributes of individuals, it thus embraces 
both attributes and individuals. The attri- 
butes of a concept constitute what is called its 
content; the individuals it embraces consti- 
tute its extent.'^ 

Accordingly, the feature of including ob- 
jects in a concept or term is called its exten- 
sion; while the feature of including attributes 
or qualities is called its intension. It follows 
as a natural consequence that the greater the 
extension of a term, the less its intension; the 
greater its intension, the less its extension. 
We will understand this more clearly when we 
consider that the more individuals contained 
in a term, the fewer common properties or 



70 Logical Thinking 

qualities it can contain ; and the more common 
properties, the fewer individuals. As Brooks 
says: ^^The concept man has more extension 
than poet, orator or statesman, since it em- 
braces more individuals; and less intension, 
since we must lay aside the distinctive attri- 
butes of poet, orator and statesman in order 
to unite them in a common class man.'*^ In 
the same way the general term animal is quite 
extended for it includes a large number of in- 
dividual varieties of very different and varied 
characteristics and qualities ; as for instance, 
the lion, camel, dog, oyster, elephant, snail, 
worm, snake, etc. Accordingly its intension 
must be small for it can include only the qual- 
ities common to all animals, which are very 
few indeed. The definition of the term shows 
how small is its intension, as: ^^ Animal. An 
organic being, rising above a vegetable in va- 
rious respects, especially in possessing sensi- 
bility, will and the power of voluntary mo- 
tion.^' Another narrows the intension still 
further when he defines animal as: *^a crea- 
ture which possesses, or has possessed, life.'' 
Halleck says: ^^ Animal is very narrow in in- 
tension, very broad in extension. There are 



Terms 71 

few qualities common to all animals, but there 
is a vast number of animals. To give the full 
meaning of the term in extension, we should 
have to name every animal, from the micro- 
scopic infuoria to the tiger, from the angle- 
worm to the whale. When we decrease the 
extension to one species of animal, horse, the 
individuals are fewer, the qualities more 
numerous. ' ' 

The importance of forming clear and dis- 
tinct concepts and of grouping, classifying 
and generalizing these into larger and broader 
concepts and terms is recognized by all au- 
thorities and is generally regarded as form- 
ing the real basis of all constructive thought. 
As Brooks says: ^^Generalization lies at the 
basis of language : only as man can form gen- 
eral conceptions is it possible for him to form 
a language. . . . Nearly all the ordinary 
words in our language are general rather than 
particular. . . • This power of generali- 
zation lies also at the basis of science. Had 
we no power of forming general ideas, each 
particular object would be a study by itself, 
and we should thus never pacs beyond the 
very alphabet of knowledge. Judgments, ex- 



72 Logical Thinking 

cept in the simplest form, would be impossi- 
ble ; and it is difficult to see how even the sim- 
plest form of the syllogism oould be con- 
structed. No general conclusion could be 
drawn from particulars, nor particular con- 
clusions from generals; and thus neither in- 
ductive nor deductive reasoning would be pos- 
sible. The classifications of science could not 
be made; and knowledge would end at the 
very threshold of science* ^^ 



CHAPTER VII. 

THE MEANING OF TERMb 

Every term has its meaning, or content, as 
some authorities prefer to call it. The word 
or words of which the term is composed are 
merely vocal sounds, serving as a symbol for 
the real meaning of the term, which meaning 
exists only in the mind of the person under- 
standing it. To one not understanding the 
meaning of the term, the latter is but as a 
meaningless sound, but to one understanding 
it the sound awakens mental associations and 
representation and thus serves its purpose as 
a symbol of thought. 

Each concrete general term has two mearir- 
ings, (1) the actual concrete thing, person or 
object to which the term is applied; and (2) 
the qualities, attributes or properties of those 
objects, persons or things in consequence of 
which the term is applied. For instance, in 
the case of the concrete term hook, the first 
meaning consists of the general idea of the 
thing which we think of as a booh, and the sec- 

73 



74 Logical Thinking 

ond meaning consists of the various qualities 
which go to make that thing a book, as the 
printed pages, the binding, the form, the 
cover, etc. Not only is that particular thing 
a book, but every other thing having the same 
or similar properties also must be a book. 
And so, whenever I call a thing a book it must 
possess the said qualities. And, whenever I 
combine the ideas of these qualities in 
thought, I must think of a book. As Jevons 
says: ^*In reality, every ordinary general 
term has a double meaning: it means the 
things to which it is applied, . • . it also 
means, in a totally different way, the qualities 
and peculiarities implied as being in the 
things. Logicians say that the number of 
things to which a term applies is the extension 
of the term ; while the number of qualities or 
peculiarities implied is the intension.^ ^ 

The extension and intension of terms has 
been referred to in the previous chapter. The 
general classification of the degrees of exten- 
sion of a general term is expressed by the two 
terms, Genus and Species, respectively. The 
classification of the character of the intension 



Meaning of Terms 75 

of a term is expressed by the term, Difference, 
Property and Accident^ respectively. 

Genus is a term indicating; *^a class of ob- 
jects containing several species; a class more 
extensive than a species ; a universal which is 
predicable of several things of different 
species. '^ 

Species is a term denoting: **a smaller class 
of objects than a genus, and of two or more 
of which a genus is composed; a predicable 
that expresses the whole essence of its sub- 
ject in so far as any common term can express 
it.'' 

An authority says : ^ ^ The names species and 
genus are merely relative and the same com- 
mon term may, in one case, be the species 
which is predicated of an individual, and in 
another case the individual of which a species 
is predicated. Thus the individual, George, 
belongs to the logical species Man, while Man 
is an individual of the logical species Animal. ' ' 
Jevons says: *^It is desirable to have names 
by which to show that one class is contained in 
another, and accordingly we call the class 
wHch is divided into two or more smaller ones, 
the genus, and the smaller ones into which it is 



76 Logical Thinking 

divided, the species/^ Animal is a genus of 
which man is a species ; while man^ in turn, is 
a genus of which Caucasian is a species ; and 
Caucasian, in turn, becomes a 5'e7^l^5 of which 
Socrates becomes a species. The student 
must avoid confusing the logical meaning of 
^ the terms genus and species with the use of 
the same terms in Natural History. Each 
class is a ^^ genus' ^ to the class helow it in ex- 
tension; and each class is a ^^ species'' to the 
class above it in extension. At the lowest ex- 
treme of the scale we reach what is called the 
infima species, which cannot be further sub- 
divided, as for instance *^ Socrates ''—this 
lowest species must always be an individual 
object, person or thing. At the highest ex- 
treme of the scale we reach what is summum 
genus, or highest genus, which is never a spe^ 
cies of anything, for there is no class higher 
than it^ as for instance, ^* being, existence, real- 
ity, truth, the absolute, the infinite, the ulti- 
mate,'' etc. Hyslop says: ^*In reality there 
is but one summum genus, while there may be 
an indefinite number of infimae species. All 
intermediate terms between these extremes 
are sometimes called subalterns, as being 



Meaning of Terms 77 

either genera or species, according to the re- 
lation in which they are viewed." 

Passing on to the classification of the char- 
acter of the intension of terms, we find : 

Difference, a term denoting: ^^The mark 
or marks by which the species is distinguished 
from the rest of the genus ; the specific char- 
acteristic.'^ Thus the color of the skin is a 
difference between the Negro and the Cau- 
casian; the number of feet the difference be- 
tween the biped and the quadruped ; the form 
and shape of leaves the difference between the 
oak and the elm trees, etc. Hyslop says: 
*^ Whatever distinguishes one object from an- 
other can be called the differentia. It is some 
characteristic in addition to the common qual- 
ities and determines the species or individual 
under the genus. ' ' 

Property, a term denoting: **A peculiar 
quality of anything ; that which is inherent in 
or naturally essential to anything." Thus a 
property is a distinguishing mark of a class. 
Thus black skin is a property of the Negro 
race ; four feet a property of quadrupeds ; a 
certain form of leaf a property of the oak tree. 



78 Logical Thinking 

Thus a difference between two species may be 
a property of one of the species. 

Accident^ a term denoting: *^Any quality 
or circumstance which may or may not belong 
to a class, accidentally as it were ; or, whatever 
does not really constitute an essential part of 
an object, person or thing. ' ^ As, for instance, 
the redness of a rose, for a rose might part 
with its redness and still be a rose— the color 
is the accident of the rose. Or, a brick may 
be white and still be a brick, although the ma- 
jority of bricks are red— the redness or white- 
ness of the brick are its accidents and not its 
essential properties. Whately says: ^^Acci- 
dents in Logic are of two kinds— separable 
and inseparable. If walking be the accident 
of a particular man, it is a separable one, for 
he would not cease to be that man though he 
stood still ; while, on the contrary, if Spaniard 
is the accident connected with him, it is an in- 
separable one, since he never can cease to be, 
ethnologically considered, what he was born.'* 

Arising from the classification of the mean- 
ing or content of terms, we find the process 
termed ^^ Definition.'' 

Definition is a term denoting: ^'An expla- 



Meaning of Terms 79 

nation of a word or term. ' * In Logic the term 
is used to denote the process of analysis in 
which the properties and differences of a term 
are clearly stated. There are of course sev- 
eral kinds of definitions. For instance, there 
is what is called a Real Definition, which 
Whately defines as: *^A definition which ex- 
plains the nature of the thing by a particular 
name.'' There is also what is called a Physi- 
cal Definition, which is: *^A definition made 
by enumerating such parts as are actually 
separable, such as the hull, masts, etc., of a 
ship.'' Also a Logical Definition, which is: 
'^A definition consisting of the genus and the 
difference. Thus if a planet be defined as *a 
wandering star,' star is the genus, and wan- 
dering points out the difference between a 
planet and an ordinary star." An Accidental 
Definition is: ^*A definition of the accidental 
qualities of a thing." An Essential Definition 
is: **a definition of the essential properties 
and differences of an object, person or thing." 
Crabbe discriminates between a Definition 
and an Explanation, as follows : ^* A definition 
is correct or precise; an explanation is gen- 
eral or ample. The definition of a word de- 



80 Logical Thinking 

fines or limits the extent of its signification; 
it is the rule for the scholar in the use of any 
word ; the explanation of a word may include 
both definition and illustration; the former 
admits of no more words than will include the 
leading features in the meaning of any term; 
the latter admits of an unlimited scope for 
diffuseness on the part of the explainer. '^ 

Hyslop gives the following excellent expla- 
nation of the Logical Definition^ which as he 
states is the proper meaning of the term in 
Logic. He states: 

*^The rules which regulate Logical Defini- 
tion are as follows : 

1. A definition should state the essential 
attributes of the species defined. 

2. A definition must not contain the name 
of word defined. Otherwise the definition is 
called a circiilus in definiendo. 

3. The definition must be exactly equiva- 
lent to the species defined. 

4. A definition should not be expressed in 
obscure, figurative, or ambiguous language. 

5. A definition must not be negative when 
it can be affirmative. '' 

A correct definition necessarily requires the 



Meaning of Terms 81 

manifestation of the two respective processes 
of Analysis and Synthesis. 

Analysis is a term denoting: ^^The separa- 
tion of anything into its constituent elements, 
qualities, properties and attributes." It is 
seen at once that in order to correctly define 
an object, person or thing, it is first necessary 
to analyze the latter in order to perceive its 
essential and accidental properties or differ- 
ences. Unless the qualities, properties and 
attributes are clearly and fully perceived, we 
cannot properly define the object itself. 

Synthesis is a term denoting: ^^The act of 
joining or putting two or more things to- 
gether ; in Logic : the method by composition, 
in opposition to the method of resolution or 
analysis.'^ In stating a definition we must 
necessarily join together the various essential 
qualities, properties and attributes, which we 
have discovered by the process of analysis; 
and the synthesized combination, considered 
as a whole, is the definition of the object ex- 
pressed by the term. 



CHAPTEE VIIL 

JUDGMENTS 

The first step in the process of reasoning 
is that of Conception or the forming of Con- 
cepts. The second step is that of Judgment, 
or the process of perceiving the agreement 
or disagreement of two conceptions. 

Judgment in Logic is defined as : ^ ^ The com- 
paring together in the mind of two notions, 
concepts or ideas, which are the objects of 
apprehension, whether complex or incomplex, 
and pronouncing that they agree or disagree 
with each other, or that one of them belongs 
or does not belong to the other. Judgment is 
therefore aflfirmative or negative.'' 

When we have in our mind two concepts, 
we are likely to compare them one with the 
other, and to thus arrive at a conclusion re- 
garding their agreement or disagreement. 
This process of comparison and decision is 
what, in Logic, is called Judgment. 

In every act of Judgment there must be at 
least two concepts to be examined and com- 

82 



Derived Judgments 83 

pared. This comparison must lead to a Judg- 
ment regarding their agreement or disagree- 
ment. For instance, we have the two con- 
cepts, horse and animal. We examine and 
compare the two concepts, and find that there 
is an agreement between them. We find that 
the concept horse is included in the higher 
concept of amimal and therefore, we assert 
that: ^^The horse is an animal/^ This is a 
statement of agreement and is, therefore, a 
Positive Judgment. We then compare the 
concepts horse and cow and find a disagree- 
ment between them, which we express in the 
statement of the Judgment that: ^^The horse 
is not a cow.'' This Judgment, stating a dis- 
agreement is what is called a Negative 
Judgment. 

In the above illustration of the comparison 
between the concepts horse and animal we find 
that the second concept animal is broader than 
the first, horse, so broad in fact that it in- 
cludes the latter. The terms are not equal, for 
we cannot say, in truth, that ^^ an animal is the 
horse." We may, however, include a part of 
the broader conception with the narrower and 
say : ^ ^ some animals are horses. ' ' Sometimes 



84 Logical Thinking 

both concepts are of equal rank, as when we 
state that: ^^Man is a rational animal." 

In the process of Judgment there is always 
the necessity of the choice between the Posi- 
tive and the Negative. When we compare the 
concepts horse and animal, we must of neces- 
sity decide either that the horse is an animal, 
or else that it is not an animal. 

The importance of the process of Judgment 
is ably stated by Halleck, as follows: ^^Were 
isolated concepts possible, they would be of 
very little use. Isolated facts are of no more 
service than unspun wool. We might have a 
concept of a certain class of three-leaved ivy, 
as we might also of poisons. Unless judg- 
ment linked these two concepts and decided 
that this species of ivy is poisonous, we might 
take hold of it and be poisoned. We might 
have a concept of bread and also one of 
meat, fruit and vegetables. If we also 
had a concept of food, unrelated to these, we 
should starve to death, for we should not think 
of them as foods. A vessel, supposing itself 
to be far out at sea, signaled another vessel 
that the crew were dying of thirst. That crew 
certainly had a concept of drinkable things 



Judgments 85 

and also of water. To the surprise of the first, 
the second vessel signaled back, ^Draw from 
the sea and drink. You are at the mouth of 
the Amazon.' The thirsty crew had not 
joined the concept drinkable to the concept of 
water over the ship's side. A man having 
taken an overdose of laudanum, his wife lost 
much valuahle time in sending out for anti- 
dotes, because certain of her concepts had not 
been connected by judgment. She had good 
concepts of coffee and of mustard; she also 
knew that an antidote to opium was needed ; 
but she had never linked these concepts and 
judged that coffee and mustard were anti- 
dotes to opium. The moment she formed that 
judgment she was a wiser woman for her 
knowledge was related and usable. . . . 
Judgment is the power revolutionizing the 
world. The revolution is slow because na- 
ture's forces are so complex, so hard to be re- 
duced to their simplest forms and so disguised 
and neutralized by the presence of other 
forces. . . • Fortunately judgment is ever 
silently working and comparing things that, 
to past ages, have seemed dissimilar; and it 
is continually abstracting and leaving out of 



86 Logical. Thinking 

the field of view those qualities which have 
simply served to obscure the point at issue. '^ 

Judgment may be both analytic or synthetic 
in its processes ; and it may be neither. When 
we compare a narrow concept with a broader 
one, as a part with a whole, the process is syn- 
thetic or an act of combination. When we 
compare a part of a concept with another con- 
cept, the process is analytic When we com- 
pare concepts equal in rank or extent, the 
process is neither synthetic nor analytic. Thus 
in the statement that : ^ ^ A horse is an animal, ' ' 
the judgment is synthetic; in the statement 
that: *^some animals are horses,'' the judg- 
ment is analytic; in the statement that: ^^a 
man is a rational animal," the judgment is 
neither analytic nor synthetic. 

Brooks says: ^^In one sense all judgments 
are synthetic. A judgment consists of the 
union of two ideas and this uniting is a process 
of synthesis. This, however, is a superficial 
view of the process. Such a synthesis is a 
mere mechanical synthesis; below this is a 
thought-process which is sometimes analytic, 
sometimes synthetic and sometimes neither 
analytic nor synthetic.'' 



Judgments 87 

The same authority states: ^^The act of 
mind described is what is known as logical 
judgment. Strictly speaking, however, every 
intelligent act of the mind is accompanied with 
a judgment. To know is to discriminate and, 
therefore, to judge. Every sensation or cog- 
nition involves a knowledge and so a judg- 
ment that it exists. The mind cannot think at 
all without judging; to think is to judge. 
Even in forming the notions which judgment 
compares, the mind judges. Every notion or 
concept implies a previous act of judgment to 
form it: in forming a concept, we compare 
the common attributes before we unite them ; 
and comparison is judgment. It is thus true 
that * Every concept is a contracted judgment; 
every judgment an expanded concept.' This 
kind of judgment, by which we affirm the 
existence of states of consciousness, discrimi- 
nate qualities, distinguish percepts and form 
concepts, is called primitive or psychological 

m 

judgment/^ 

In Logical Judgment there are two aspects ; 
i. e., Judgment by Extension and Judgment by 
Intension. When we compare the two con- 
cepts horse and animal we find that the con- 



88 Logical. Thin^king 

cept horse is contained in the concept animal 
and the judgment that ''a horse is an anirmiV' 
may be considered as a Judgment by Exten- 
sion. In the same comparison we see that the 
concept horse contains the quality of animal- 
ity, and in attributing this quality to the horse ^ 
we may also say ^^the horse is an animal/^ 
which judgment may be considered as a Judg- 
ment by Intension. Brooks says: ^^Both 
views of Judgment are correct ; the mind may 
reach its judgment either by extension or by 
intension. The method by extension is usually 
the more natural.'' 

When a Judgment is expressed in words it 
is called a Proposition. There is some con- 
fusion regarding the two terms, some holding 
that a Judgment and a proposition are identi- 
cal, and that the term ^^proposition" may be 
properly used to indicate the judgment itself. 
But the authorities who seek for clearness of 
expression and thought now generally hold 
that : 'M Proposition is a Judgment expressed 
in words/ ^ In the next chapter, in which we 
consider Propositions, we shall enter into a 
more extended consideration of the subject of 
Judgments as expressed in Propositions, 



Judgments 89 

which consideration we omit at this point in 
order to avoid repetition. Jnst as the re- 
spective subjects of Concepts and Terms nec- 
essarily blend into each other, so do the re- 
spective subjects of Judgments and Propo- 
sitions. In each case, too, there is the ele- 
ment of the mental process on the one hand 
and the verbal expression of it on the other 
hand. It will be well to keep this fact in mind. 



CHAPTER IX. 

PROPOSITIONS 

We have seen that the first step of Deduct- 
ive Reasoning is that which we call Concepts. 
The second step is that which we call 
Propositions. 

In Logic, a Proposition is: ^' A sentence, or 
part of a sentence, affirming or denying a con- 
nection between the terms ; limited to express 
assertions rather than extended to questions 
and commands.^' Hyslop defines a Propo- 
sition as: ^^any affirmation or denial of an 
agreement between two conceptions.'' 

Examples of Propositions are found in the 
following sentences: **The rose is a flower;'' 
*^a horse is an animal;" *^ Chicago is a city;" 
all of which are affirmations of agreement be- 
tween the two terms involved; also in: *^A 
horse is not a zebra;" '^ pinks are not roses ;" 
*^the whale is not a fish;" etc., which are 
denials of agreement between the terms. 

The Parts of a Proposition are: (1) the 
Subject, or that of which something is af- 

90 



Pbopositions 91 

firmed or denied; (2) the Predicate, or the 
something which is affirmed or denied regard- 
ing the Subject; and (3) the Copula, or the 
verb serving as a link between the Subject and 
the Predicate. 

In the Proposition: ^^Man is an animal/' 
the term man is the Subject ; the term an ani- 
mal is the Predicate ; and the word is, is the 
Copula. The Copula is always some form of 
the verb to he, in the present tense indicative, 
in an affirmative Proposition; and the same 
with the negative particle affixed, in a nega- 
tive Proposition. The Copula is not always 
directly expressed by the word is or is not, 
etc., but is instead expressed in some phrase 
w3iich implies them. For instance, we say ' ^ he 
runs,'' which implies ^^he is running." In 
the same way, it may appear at times as if 
the Predicate was missing, as in: *^God is," 
by which is meant ^ ^ Grod is existing. ' ' In some 
cases, the Proposition is inverted, the Predi- 
cate appearing first in order, and the Subject 
last, as in: ^'Blessed are the peacemakers;" 
or ^^ Strong is Truth." In such cases judg- 
ment must be used in determining the matter, 



92 Logical Thinking 

in accordance with the character and meaning 
of the terms. 

An Affirmative Proposition is one in which 
the Predicate is affirmed to agree with the 
Subject. A Negative Proposition is one in 
which the agreement of the Predicate and 
Subject is denied. Examples of both of these 
classes have been given in this chapter. 

Another classification of Propositions di- 
vides them in three classes, as follows (1) 
Categorical; (2) Hypothetical; (3) Dis- 
junctive. 

A Categorical Proposition is one in which 
the affirmation or denial is made without 
reservation or qualification, as for instance: 
^^Man is an animal ;'' ^Hhe rose is a flower,'^ 
etc. The fact asserted may not be true, but 
the statement is made positively as a state- 
ment of reality. 

A Hypothetical Proposition is one in which 
the affirmation or denial is made to depend 
upon certain conditions, circumstances or sup-, 
positions, as for instance: ^^If the water is 
boiling-hot, it will scald;" or **if the powder 
be damp, it will not explode,'' etc. Jevons 
says: ^^Hypothetical Propositions may gen- 



Propositions 93 

erally be recognized by containing the little 
word ^if;^ but it is doubtful whether they 
really differ much from the ordinary proposi- 
tions. . . . We may easily say that * boil- 
ing waiter will scald/ and ^damp gunpowder 
will not explode, ' thus avoiding the use of the 
word 4f/ '' 

A Disjunctive Proposition is one ^^ implying 
or asserting an alternative," and usually con- 
taining the conjunction *^or,'' sometimes to- 
gether with ^ ^ either, "as for instance : ' ^ Light- 
ning is sheet or forked;" ^^ Arches are either 
round or pointed ; " ^ * Angles are either obtuse, 
right angled or acute." 

Another classification of Propositions di- 
vides them in two classes as follows: (1) Uni- 
versal; (2) Particular. 

A Universal Proposition is one in which the 
whole quantity of the Subject is involved in 
the assertion or denial of the Predicate. For 
instance: *^A11 men are liars," by which is 
affirmed that all of the entire race of men are 
in the category of liars, not some men but all 
the men that are in existence. In the same 
way the Proposition : ^^No men are immortal" 
is Universal, for it is a universal denial. 



94 Logical Tnii^KiNG 

A Particular Proposition is one in which the 
affirmation or denial of the Predicate involves 
only a part or portion of the whole of the Sub- 
ject, as for instance: ''Some men are athe- 
ists," or ''Some women are not vain," in 
which cases the affirmation or denial does not 
involve all or the whole of the Subject. Other 
examples are: ^^A few men," etc.; ^^many 
people," etc.; "certain books," etc.; "most 
people," etc. 

Hyslop says : ' ' The signs of the Universal 
Proposition, when formally expressed, are 
all, every, each, any, and ivhole or words with 
equivalent import. The signs of Particular 
Propositions are also certain adjectives of 
quantity, such as some, certain, a few, many, 
most or such others as denote at least a part 
of a class. 

The subject of the Distribution of Terms in 
Propositions is considered very important by 
Logicians, and as Hyslop says : ' ' has much im- 
portance in determining the legitimacy, or at 
least the intelligibility, of our reasoning and 
the assurance that it will be accepted by 
others." Some authorities favor the term, 
** Qualification of the Terms of Propositions," 



Pbopositions 95 

but the established usage favors the term 
** Distribution/* 

The definition of the Logical term, ^^Dis- 
tribution/* is: ^^The distinguishing of a uni- 
versal whole into its several kinds of species ; 
the employment of a term to its fullest extent; 
the application of a term to its fullest extent, 
so as to include all significations or applica- 
tions." A Term of a Proposition is distrib- 
uted when it is employed in its fullest sense ; 
that is to say, when it is employed so as to ap- 
ply to each and every object^ person or thing 
included under it. Thus in the proposition, 
^^ AH horses are animals," the term horses is 
distributed; and in the proposition, ^^Some 
horses are thoroughbreds," the term horses is 
not distributed. Both of these examples re- 
late to the distribution of the subject of the 
proposition. But the predicate of a proposi- 
tion also may or may not be distributed. For 
instance, in the proposition, ^^All horses are 
animals," the predicate, animals, is not dis- 
tributed, that is, not used in its fullest sense, 
for all animals are not horses— \hQve are some 
animals which are not horses and, therefore, 
the predicate, animals, not being used in its 



96 Logical Thinking 

fullest sense is said to be ^^not distributed.^' 
The proposition really means : ^ ^ All horses are 
some animals/' 

There is however another point to be re- 
membered in the consideration of Distribution 
of Terms of Propositions, which Brooks ex- 
presses as follows: ^^Distribution generally 
shows itself in the form of the expression, but 
sometimes it may be determined by the 
thought. Thus if we say, ^Men are mortal,' 
we mean all men, and the term men is distrib- 
uted. But if we say ^ Books are necessary to 
a library,' we mean, not *all books' but *some 
books. ' The test of distribution is whether the 
term applies to ^each and every/ Thus when 
we say *men are mortal,' it is true of each and 
every man that he is mortal." 

The Rules of Distribution of the Terms of 
Proposition are as follows : 

1. All universals distribute the subject. 

2. All particulars do not distribute the 
subject. 

3. All negatives distribute the predicate. 

4. All affirmatives do not distribute the 
predicate. 

The above rules are based upon logical rea- 



Propositions 97 

soning. The reason for the first two rules is 
quite obvious, for when the subject is univer- 
sal, it follows that the whole subject is ir.- 
volved; when the subject is particular it fol- 
lows that only a part of the subject is involved. 
In the case of the third rule, it will be seen 
that in every negative proposition the whole of 
the predicate must be denied the subject, as 
for instance, when we say : ^ ^ Some animals are 
not horses^ ' ' the whole class of horses is cut off 
from the subject, and is thus distributed. In 
the case of the fourth rule, we may readily see 
that in the affirmative proposition the whole 
of the predicate is not denied the subject, as 
for instance, when we say that: ^^ Horses are 
animals," we do not mean that horses are all 
the animals, but that they are merely a part or 
portion of the class animal—therefore, the 
predicate, animals, is not distributed. 

In addition to the forms of Propositions 
given there is another class of Propositions 
known as Definitive or Substitutive Proposi- 
tions, in which the Subject and the Predicate 
are exactly alike in extent and rank. For in- 
stance, in the proposition, ^^A triangle is a 
polygon of three sides'^ the two terms are in- 



98 Logical Thinking 

terchangeable ; tliat is, may be substituted for 
each other. Hence the term ^^ substitutive/^ 
The term *^ definitive '^ arises from the fact 
that the respective terms of this kind of a 
proposition necessarily define each other. All 
logical definitions are expressed in this last 
mentioned form of proposition, for in such 
cases the subject and the predicate are pre- 
cisely equal to each other. 



CHAPTER X. 

IMMEDIATE REASONING 

In the process of Judgment we must com- 
pare two concepts and ascertain their agree- 
ment of disagreement. In the process of 
Eeasoning we follow a similar method and 
compare two judgments, the result of such 
comparison being the deduction of a third 
judgment. 

The simplest form of reasoning is that 
known as Immediate Eeasoning, by which is 
meant^the deduction of one proposition from 
another which implies it. Some have defined 
it as: ^^ reasoning without a middle term/^ 
In this form of reasoning only one proposition 
is required for the premise, and from that 
premise the conclusion is deduced directly and 
without the necessity of comparison with any 
other term of proposition. 

The two principal methods employed in this 
form of Reasoning are; (1) Opposition; (2) 
Conversion. 

Opposition exists between propositions hav- 

: 99 



100 Logical Thinking 

ing tlie same subject and predicate, but differ- 
ing in quality or quantity, or both^ The Laws 
of Opposition are as follows : 

L (1) If the universal is true, the particu- 
lar is true. (2) If the particular is false, the 
universal is false. (3) If the universal is 
false, nothing follows. (4) If the particular 
is true, nothing follows. 

II. (1) If one of two contraries is true, 
the other is false. (2) If one of two contra- 
ries is false, nothing can be inferred. (3) 
Contraries are never both true, but both may 
be false. 

III. (1) If one of two sub-contraries is 
false, the other is true. (2) If one of two sub- 
contraries is true, nothing can be inferred con- 
cerning the other. (3) Sub-contraries can 
never be both false, but both may be true. 

IV. (1) If one of two contradictories is 
true, the other is false. (2) If one of two con- 
tradictories is false, the other is true. (3) 
Contradictories can never be both true or both 
false, but always one is true and the other is 
false. 

In order to comprehend the above laws, the 
student should familiarize himself with the 



Immediate Eeasoning 



101 



following arrangement, adopted by logicians 



as a convenience: 



Propositions 



Universal J^"^^*^^^ (^> 

Negative (E) 

AjBfirmative (I) 

Negative (0) 



Particular 



Examples of the above : Universal Affirma- 
tive (A): ^^AU men are mortal;" Universal 
Negative (E) : ^^No man is mortal;" ^^Par- 
ticular Affirmative (I): *'Some men are 
mortal;" Particular Negative (0): ^^Some 
men are not mortal." 

The following examples of abstract prop- 
ositions are often used by logicians as tend- 
ing toward a clearer conception than ex- 
amples such as given above : 

(A) ^^AUAisB," 

(I) ^^SomeAisB." 

(E) ^^No A is B.'' 

(0) ^^SomeAisnotB." 

These four forms of propositions bear cer- 
tain logical relations to each other, as follows : 

A and E are styled contraries. I and are 
sub-contraries; A and I and also E and are 



102 



Logical Thinking 



called subalterns; A and and also I and E 
are styled contradictories. 

A close study of these relations, and the 
symbols expressing them, is necessary for a 
clear comprehension of the Laws of Opposi- 
tion stated a little further back, as well as the 
principles of Conversion which we shall men- 
tion a little further on. The following chart, 
called the Square of Opposition, is also em- 
ployed by logicians to illustrate the relations 
between the four classes of propositions : 




Conversion is the process of immediate 
reasoning by which we infer from a given 
proposition another proposition^ having the 



Immediate Reasoning 103 

predicate of the original for its subject, and 
the subject of the original for its predicate ; or 
stated in a few words: Conversion is the 
transposition of the subject and predicate of 
a proposition. As Brooks states it : ^ * Proposi- 
tions or judgments are converted when the 
subject and predicate change places in such a 
manner that the resulting judgment is an in- 
ference from the given judgment.'' The new 
proposition, resulting from the operation or 
Conversion, is called the Converse; the orig- 
inal proposition is called the Convertend. 

The Law of Conversion is that: ^*No term 
must be distributed in the Converse that is 
not distributed in the Convertend." This 
arises from the obvious fact that nothing 
should be afl&rmed in the derived proposition 
than there is in the original proposition. 

There are three kinds of Conversion; viz: 
(1) Simple Conversion; (2) Conversion by 
Limitation; (3) Conversion by Contraposi- 
tion. 

In Simple Conversion there is no change in 
either quality or quantity. In Conversion hy 
Limitation the quality is changed from uni- 
versal to particular. In Conversion by Nega- 



104 Logical Thinking 

tion the quality is changed but not the quan- 
tity. Referring to the classification tables 
and symbols given in the preceding pages of 
this chapter, we may now proceed to consider 
the application of these methods of Conver- 
sion to each of the four kinds of propositions ; 
as follows : 

The Universal Affirmative (symbol A) 
proposition is converted by Limitation, or by 
a change of quality from universal to particu- 
lar. The predicate not being ^^distributed'' in 
the convertend, we must not distribute it in 
the converse by saying ^^all/^ Thus in this 
case we must convert the proposition, *^all 
men are mortaP' (A), into ^^some mortals are 
men" (I). 

The Universal Negative (symbol E) is con- 
verted by Simple Conversion, in which there 
is no change in either quality or quantity. For 
since both terms of *^E'' are distributed, they 
may both be distributed in the converse with- 
out violating the law of conversion. Thus 
'^No man is mortal'' is converted into: *'Na 
mortals are men." ^^E" is converted into 

The Particular Affirmative (symbol I) is 



Immediate Reasoning 105 

also converted by Simple Conversion in which 
there is no change in either quality or quan- 
tity. For since neither term is distributed in 
*^I/' neither term may be distributed in the 
converse, and the latter must remain ^^I/' 
For instance; the proposition: **Some men 
are mortal" is converted into the proposition, 
**Some mortals are men." 

The Particular Negative (symbol 0) is con- 
verted by Conversion by Negation, in which 
the quality is changed but not the quantity. 
Thus in converting the proposition: ^*Some 
men are not mortal," we must not say ^^some 
mortals are not men," for in so doing we 
would distribute men in the predicate, where 
it is not distributed in the convertend. Avoid- 
iug this, we transfer the negative particle from 
the copula to the predicate so that the conver- 
tend becomes ^*I" which is converted by 
Simple Conversion. Thus we transfer ^ ^ Some 
men are not mortal ' ' into * ^ Some men are not- 
mortal" from which we easily convert (by 
simple Conversion) the proposition: **Some 
not-mortals are men." 

It will be well for students, at this point, to 
consider the three following Fundamental 



106 Logical Thiistkii^g 

Laws of Thought as laid down by the authori- 
ties, which are as follows: 

The Law of Identity ^ which states that: 
^^The same quality or thing is always the 
same quality or thing, no matter how different 
the conditions in which it occurs.'' 

The Law of Contradiction, which states 
that: *^No thing can at the same time and 
place both be and not be.'' 

The Law of Excluded Middle, which states 
that: ^^ Everything must either be or not be; 
there is no other alternative or middle 
course." 

Of these laws. Prof. Jevons, a noted author- 
ity, says : ' ' Students are seldom able to see at 
first their full meaning and importance. All 
arguments may be explained when these self- 
evident laws are granted; and it is not too 
much to say that the whole of logic will be 
plain to those who will constantly use these 
laws as the key." 



CHAPTER XI. 

INDUCTIVE BEASONING 

Inductive Eeasoning, as we have said, is 
the process of discovering general truth from 
particular truths, or inferring general laws 
from particular facts. Thus, from the experi- 
ence of the individual and the race regarding 
the particular truth that each and every man 
under observation has been observed to die 
sooner or later, it is inferred that all men die, 
and hence, the induction of the general truth 
that ^^AU men must die,'' Or, as from ex- 
perience we know that the various kinds of 
metals expand when subjected to heat, we in- 
fer thsit all metals are subject to this law, and 
that consequently we may arrive by inductive 
reasoning at the conclusion that: **A11 metals 
expand when subjected to heat.'' It will be 
noticed that the conclusion arrived at in this 
way by Inductive Reasoning forms the funda- 
mental premise in the process of Deductive 
Eeasoning. As we have seen elsewhere, the 
two processes. Inductive and Deductive Rea- 

107 



108 Logical Thinking 

soning, respectively are interdependent— restr 
ing upon one another. 

Jevons says of Inductive Eeasoning: *^In 
Deductive Eeasoning we inquire bow we may 
gather the truth contained in some proposi- 
tions called Premises, and put into another 
proposition called the Conclusion. We have 
not yet undertaken to find out how we can learn 
what propositions really are true, but only 
what propositions are true when other ones 
are true. All the acts of reasoning yet con- 
sidered would be called deductive becmise we 
deduce, or lead doivn the. truth from premises 
to conclusion. It is an exceedingly important 
thing to understand deductive inference cor- 
rectly, but it might seem to be still more im- 
portant to understand inductive inference, by 
which we gather the truth of general proposi- 
tions from facts observed as happening in the 
world around us.'' Halleck says: **Man has 
to find out through his own experience, or that 
of others, the major premises from which he 
argues or draws his conclusions. By induc- 
tion we examine what seems to us a suiB&cient 
number of individual cases. We then con- 
clude that the rest of these cases, which we 



Inductive Reasoning 109 

have not examined, will obey the same general 
law. . . . Only after general laws have 
been laid down, after objects have been classi- 
fied, after major premises have been formed, 
can deduction be employed. ' ' 

Strange as may now appear, it is a fact that 
until a comparatively recent period in the 
history of man, it was held by philosophers 
that the only way to arrive at all knowledge 
was by means of Deductive Eeasoning, by the 
use of the Syllogism. The influence of Aris- 
totle was great and men preferred to pursue 
artificial and complicated methods of Deduct- 
ive Reasoning, rather than to reach the truth 
by obtaining the facts from Nature herself, 
at first hand, and then inferring general prin- 
ciple from the facts so gathered. The rise of 
modern scientific methods of reasoning, along 
the lines of Inductive Inference, dates from 
about 1225-1300. Roger Bacon was one of the 
first to teach that we must arrive at scientific 
truth by a process of observation and experi- 
mentation on the natural objects to be found 
on all sides. He made many discoveries by 
following this process. He was ably seconded 
by Galileo who lived some three hundred 



110 Logical. Thinking 

years later, and who also taught that many 
great general truths might be gained by care- 
ful observation and intelligent inference. 
Lord Francis Bacon, who lived about the same 
time as Galileo, presented in his Novum Or- 
ganum many excellent observations and facts 
regarding the process of Inductive Eeasoning 
and scientific thought. As Jevons says: *^ In- 
ductive logic inquires by what manner of rea- 
soning we can gather the laws of nature from 
the facts and events observed. Such reason- 
ing is called induction, or inductive inquiry, 
and, as it has actually been practiced by all 
the great discoverers in science, it consists in 
four steps.'' 

The Four Steps in Inductive Reasoning, as 
stated by Jevons, are as follows : 

First /S^e^?.— Preliminary observation. 

Second Step.— The making of hypotheses.^ 

Third /Siep.— Deductive reasoning. 

Fourth /S'^e^^.— Verification. 

It will be seen that the process of Inductive 
Eeasoning is essentially a synthetic process, 
because it operates in the direction of combin- 
ing and uniting particular facts or truths into 
general truths or laws which comprehend, 



Inductive Reasoning 111 

embrace and include them all. As Brooks 
&ays: ^^The particular facts are united by the 
mind into the general law ; the general law em- 
braces the particular facts and binds them 
together into a unity of principle and thought. 
Induction is thus a process of thought from 
the parts to the whole— a synthetic process. '^ 
It will also be seen that the process of Induct- 
ive Reasoning is essentially an ascending 
process, because it ascends from particular 
facts to general laws; particular truths to 
universal truths ; from the lower to the higher, 
the narrower to the broader, the smaller to the 
greater. 

Brooks says of Inductive Reasoning : ^ ' The 
relation of induction to deduction will be 
clearly seen. Induction and Deduction are 
the converse, the opposites of each other. De- 
duction derives a particular truth from a 
general truth; Induction derives a general 
truth from particular truths. This antithesis 
appears in every particular. Deduction goes 
from generals to particulars ; Induction goes 
from particulars to generals. Deduction is 
an analytic process ; Induction is a synthetic 
process. Deduction is a descending process— 



112 LoGiCAii Thinking 

it goes from the higher truth to the lower 
truth; Induction is an ascending process— it 
goes from the lower truth to the higher. They 
differ also in that Deduction may be applied 
to necessary truths, while Induction is mainly 
restricted to contingent truths.'^ Hyslop 
says : ^ ' There have been several ways of de- 
fining this process. It has been usual to con- 
trast it with Deduction. Now, deduction is 
often said to be reasoning from general to par- 
ticular truths, from the containing to the con- 
tained truth, or from cause to effect. Induc- 
tion, therefore, by contrast is defined as rea- 
soning from the particular to the general, 
from the contained to the containing, or from 
effect to cause. Sometimes induction is said 
to be reasoning from the known to the un- 
known. This would make deduction, by con- 
trast, reasoning from the unknown to the 
known, which is absurd. The former ways of 
representing it are much the better. But 
there is still a better way of comparing them. 
Deduction is reasoning in which the conclusion 
is contained in the premises. This is a ground 
for its certitude and we commit a fallacy when- 
ever we go beyond the premises as shown by 



Inductive Eeasoning 113 

the laws of the distribution of terms. In con- 
trast with this, then, we may call inductive 
reasoning the process by which we go beyond 
the premises in the conclusion. . . . The 
process here is to start from given facts and 
to infer some other probable facts more gen- 
eral or connected with them. In this we see 
the process of going beyond the premises. 
There are, of course, certain conditions which 
regulate the legitimacy of the procedure, just 
as there are conditions determining deduction. 
They are that the conclusion shall represent 
the same general kind as the premises, with a 
possibility of accidental differences. But it 
goes beyond the premises in so far as known 
facts are concerned.-' 

The following example may give you a 
clearer idea of the processes of Inductive 
Eeasoning : 

First Step. Preliminary Observation. Ex- 
ample: We notice that all the particular 
magnets which have come under our observa- 
tion attract iron. Our mental record of the 
phenomena may be stated as: '^ A, B, C, D, E, 
F, Gr, etc., and also X, Y, and Z, all of which 



114 Logical Thinking 

are magnets, in all observed instances, and at 
all observed times, attract iron/^ 

Second Step. The Making of Hypotheses. 
Example : Upon the basis of the observations 
and experiments, as above stated, and apply- 
ing the axiom of Inductive Eeasoning, that: 
*'What is true of the many, is true of the 
whole, ' ' we feel justified in forming a hypothe- 
sis or inference of a general law or truth, ap- 
plying the facts of the particulars to the gen- 
eral, whole or universal, thus: ^^All magnets 
attract iron. ' ' 

Third Step. Deductive Reasoning. Exam- 
ple : Picking up a magnet regarding which we 
have had no experience and upon which we 
have made no experiments, we reason by the 
syllogism, as follows: (1) All magnets attract 
iron; (2) This thing is a magnet; therefore 
(3) This thing will attract iron. In this we 
apply the axiom of Deductive Eeasoning: 
^^ Whatever is true of the whole is true of the 
parts.'* 

Fourth Step. Verification. Example: We 
then proceed to test the hypothesis upon the 
particular magnet, so as to ascertain whether 
or not it agrees with the particular facts. If 



Inductive Reasoning 115 

the magnet does not attract iron we know that 
either our hypothesis is wrong and that some 
magnets do not attract iron; or else that our 
judgment regarding that particular ^^ thing" 
being a magnet is at fault and that it is not 
a magnet. In either case, further examina- 
tion, observation and experiment is necessary. 
In case the particular magnet does attract 
iron, we feel that we have verified our hypothe- 
sis and our judgment. 



CHAPTEE XII. 

KEASONING BY INDUCTION- 

The term ^^ Induction," in its logical usage, 
is defined as follows: '' (a) The process of in- 
vestigating and collecting facts; and (b) the 
deducing of an inference froinl these facts; 
also (c) sometimes loosely used in the sense 
of an inference from observed facts." Mill 
says: ^^ Induction ^ then, is that operation of 
the mind, by which we infer that what we 
know to be true in a particular case or cases, 
will be true in all cases which resemble the 
former in certain assignable respects. In other 
words, Induction is the process by which we 
conclude that what is true of certain individ- 
uals of a class, is true of the whole class, or 
that what is true at certain times will be 
true in similar circumstances at all times. ' ' 

The Basis of Induction is the axiom that : 
^^What is true of the many is true of the 
whole.^^ Esser, a well known authority, states 
this axiom in rather more complicated form, 
as follows: ^'That which belongs or does not 

116 



Reasoning by Induction 117 

belong to nuany things of tlie same Mnd, be- 
longs or does not belong to all things of the 
same kind.'' 

This basic axiom of Induction rests upon 
the conviction that Nature's laws and mani- 
festations are regular, orderly and uniform. 
If we assume that Nature does not manifest 
these qualities, then the axiom must fall, and 
all inductive reason must be fallacious. As 
Brooks well says: ^^ Induction has been com- 
pared to a ladder upon which we ascend from 
facts to laws. This ladder cannot stand un- 
less it has something to rest upon; and this 
something is our faith in the constancy of Na- 
ture 's laws. ' ' Some authorities have held that 
this perception of the uniformity of Nature's 
laws is in the nature of an intuitive truth, or an 
inherent law of our intelligence. Others hold 
that it is in itself an inductive truth, arrived 
at by experience and observation at a very 
early age. We are held to have noticed the 
uniformity in natural phenomena, and alm'ost 
instinctively infer that this uniformity is con- 
tinuous and universal. 

The authorities assume the existence of two 
kinds of Induction, namely: (1) Perfect In- 



118 Logical Thinking 

duction; and (2) Imperfect Induction. Other, 
but similar, terms are employed by different 
authorities to designate these two classes. 

Perfect Induction necessitates a knowledge 
of all the particulars forming a class; that is, 
all the individual objects, persons, things or 
facts comprising a class must be known and 
enumerated in this form of Induction. For 
instance, if we hnew positively all of Brown ^s 
children, and that their names were John, 
Peter, Mark, Luke, Charles, William, Mary 
and Susan, respectively; and that each and 
every one of them were freckled and had red 
hair ; then, in that case, instead of simply gen- 
eralizing and stating that: ^^John, Peter, 
Mark, Luke, Charles, William, Mary and 
Susan, who are all of Brown's children, are 
freckled and have red hair,'' we would save 
words, and state the inductive conclusion: 
^^All Brown's children are freckled and have 
red hair. ' ' It will be noticed that in this case 
we include in the process only what is stated 
in the premise itself , and we do not extend our 
inductive process beyond the actual data upon 
which it is based. This form of Induction is 
sometimes called *^ Logical Induction," be- 



Eeasoning by Induction 119 

cause the inference is a logical necessity, with- 
out the possibility of error or exception. By 
some authorities it is held not to be Induction 
at all, in the strict sense, but little more than 
a simplified form of enumeration. In actual 
practice it is seldom available, for it is almost 
impossible for us to know all the particulars 
in inferring a general law or truth. In view of 
this difficulty, we fall back upon the more 
practical form of induction known as : 

Imperfect Induction, or as it is sometimes 
called ^^ Practical Induction,'' by which is 
meant the inductive process of reasoning in 
which we assume that the particulars or facts 
actually known to us correctly represent those 
which are not actually known, and hence the 
whole class to which they belong. In this 
process it will be seen that the conclusion ex- 
tends beyond the data upon which it is based. 
In this form of Induction we must actually 
employ the principle of the axiom: ^'What is 
true of the many is true of the whole''— that 
is, must assume it to be a fact, not because we 
know it by actual experience, but because we 
infer it from the axiom which also agrees with 
past experience. The conclusion arrived at 



120 LoGicAii Thii^king 

may not always be true in its fullest sense, as 
in the case of the conclusion of Perfect Induc- 
tion, but is the result of an inference based 
upon a principle which gives us a reasonable 
right to assume its truth in absence of better 
knowledge. 

In considering the actual steps in the proc- 
ess of Inductive Eeasoning we can do no bet- 
ter than to follow the classification of 
Jevons, mentioned in the preceding chapter, 
the same being simple and readily compre- 
hended, and therefore preferable in this case 
to the more technical classification favored by 
some other authorities. Let us now consider 
these four steps. 

First Step. Preliminary observation. It 
follows that without the experience of oneself 
or of others in the direction of observing and 
remembering particular facts, objects, per- 
sons and things, we cannot hope to acquire 
the preliminary facts for the generalization 
and inductive inference necessary in Induct- 
ive Eeasoning. It is necessary for us to form 
a variety of clear Concepts or ideas of facts, 
objects, persons and things, before we may 
hope to generalize from these particulars. In 



Reasonikg by Induction 121. 

the chapters of this book devoted to the con- 
sideration of Concepts, we may see the funda- 
mental importance of the formation and ac- 
quirement of correct Concepts. Concepts are 
the fundamental material for correct reason- 
ing. In order to produce a perfect finished 
product, we must have perfect materials, and 
a sufficient quantity of them. The greater the 
knowledge one possesses of the facts and ob- 
jects of the outside world, the better able is 
he to reason therefrom. Concepts are the raw 
material which must feed the machinery of 
reasoning, and from which the final product 
of perfected thought is produced. As Hal- 
leck says: ^' There must first be a presentar 
tion of materials. Suppose that we wish to 
form the concept fruit. We must first per- 
ceive the different kinds of fruit— cherry, 
pear, quince, plum, currant, apple, fig, orange, 
etc. Before we can take the next step, we 
must be able to form distinct and accurate 
images of the various kinds of fruit If the 
concept is to be absolutely accurate, not one 
kind of fruit must be overlooked. Practically 
this is impossible ; but many kinds should be 
examined. Where perception is inaccurate 



122 Logical Thinking 

and stinted, the products of thought cannot be 
trustworthy. No building is firm if reared on 
insecure foundations.'' 

In the process of Preliminary Observation, 
we find that there are two ways of obtaining 
a knowledge of the facts and things around 
us. These two ways are as follows : 

I. By Simple Observation, or the percep- 
tion of the happenings which are manifested 
without our interference. In this, way we 
perceive the motion of the tides; the move- 
nient of the planets; the phenomena of the 
weather; the passing of animals, etc. 

II. By the Observation of Experiment^ or 
the perception of happenings in which we in- 
terfere with things and then observe the re- 
sult. An experiment is: *^A trial, proof, or 
test of anything ; an act, operation, or process 
designed to discover some unknown truth, 
principle or effect, or to test some received 
or reputed truth or principle." Hobbes says : 
^^To have had many experiments is what we 
call experience. ' ' Jevons says : ^ ' Experi- 
mentation is observation with something 
more ; namely, regulation of the things whose 
behavior is to be observed. The advantages 



Reasoning by Induction 123 

of experiment over mere observation are of 
two kinds. In the first place, we shall gener- 
ally know much more certainly and accurately 
with what we are dealing, when we make ex- 
periments than when we simply observe nat- 
ural events. ... It is a further advan- 
tage of artificial experiments, that they en- 
able us to discover entirely new substances 
and to learn their properties. ... It 
would be a mistake to suppose that the mak- 
ing of an experiment is inductive reasoning, 
and gives us without further trouble the laws 
of nature. Experiments only give us the facts 
upon which we may afterward reason. . . . 
Experiments then merely give facts, and it is 
only by careful reasoning that we can learn 
when the same facts will be observed again. 
The general rule is that the same causes will 
produce the same effects. Whatever happens 
in one case will happen in all like cases, pro- 
vided that they are really like, and not merely 
apparently so. . . . When we have by re- 
peated experiments tried the effect which all 
the surrounding things might have on the re- 
sult, we can then reason with much confidence 
as to similar results in similar circumstances. 



124 Logical Thinking 

. . . In order that we may, from our obser- 
vations and experiments, learn the law of na- 
ture and become able to foresee the future, we 
must perform the process of generalization. 
To generalize is to draw a general law from 
particular cases, and to infer that what we see 
to be true of a few things is true of the whole 
genus or class to which these things belong. 
It requires much judgment and skill to gener- 
alize correctly, because everything depends 
upon the number and character of the in- 
stances about which we reason.'* 

Having seen that the first step in Inductive 
Eeasoning is Preliminary Observation, let us 
now consider the next steps in which we may 
see what we do with the facts and ideas which 
we have acquired by this Observation and 
Experiment. 



CHAPTER XIII. ^ ' 

THEOEY AND HYPOTHESES 

Following Jevons' classification, we find 
that the Second Step in Inductive Reasoning 
is that called ^^The Making of Hypotheses.'' 

A Hypothesis is: ^^A supposition, proposi- 
tion or principle assumed or taken for granted 
in order to draw a conclusion or inference in 
proof of the point or question ; a proposition 
assumed or taken for granted, though not 
proved, for the purpose of deducing proof of 
a point in question." It will be seen that a 
Hypothesis is merely held to be possibly or 
probably true, and not certainly true; it is in 
the nature of a working assumption, whose 
truth must be tested by observed facts. The 
assmnption may apply either to .the cause of 
things, or to the laws which govern things. 
Akin to a hypothesis, and by many people 
confused in meaning with the latter, is what 
is called a Theory. 

A Theory is : ^^ A verified hypothesis ; a hy- 
pothesis which has been established as, ap- 

125 



126 Logical. Thinking 

parently, the true one/' An authority says 
^^ Theory is a stronger word than hypotJiesis. 
A theory is founded on principles which have 
been established on independent evidence. A 
hypothesis merely assumes the operation of a 
cause which would account for the phenom- 
ena, but has not evidence that such cause 
was actually at work. Metaphysically, a 
theory is nothing but a hypothesis supported 
by a large amount of probable evidence.'' 
Brooks says: ^^When a hypothesis is shown 
to explain all the facts that are known, these 
facts being varied and extensive, it is said to 
be verified, and becomes a theory. Thus we 
have the theory of universal gravitation, the 
Copernican theory of the solar system, the 
undulatory theory of light, etc., all of which 
were originally mere hypotheses. This is the 
manner in which the term is usually em- 
ployed in the inductive philosophy; though it 
must be admitted that it is not always used 
in this striot sense. Discarded hypotheses are 
often referred to as theories; and that which 
is actually a theory is sometimes called a 
hypothesis." 
The steps by which we build up a hypothe- 



Theory and Hypotheses 127 

sis are numerous and varied. In the first 
place we may erect a hypothesis by the 
methods of what we have described as Perfect 
Induction, or Logical Induction. In this case 
we proceed by simiple generalization or simple 
enumeration. The example of the freckled, 
red-haired children of Brown, mentioned in a 
previous chapter, explains this method. It re- 
quires the examination and knowledge of 
every object or fact of which the statement 
or hypothesis is made. Hamilton states that 
it is the only induction which is absolutely 
necessitated by the laws of thought. It does not 
extend further than the plane of experience. 
It is akin to mathematical reasoning. 

Far more important is the process by which 
hypotheses are erected by means of inferences 
from Imperfect Induction, by which we reason 
from the known to the unknown, transcend- 
ing experience, and making true inductive 
inferences from the axiom of Inductive E6a- 
soning. This process involves the subject of 
Causes. Jevons says : * ^ The cause of an event 
is that antecedent, or set of antecedents, from 
which the event always follows. People often 
make much difficulty about understanding 



128 Logical Thinking 

what the cause of an event means, bnt it really 
means nothing beyond the things that must 
exist before in order that the event shall hap-- 
pen afterward/^ 

Causes are often obscure and dilBficult to 
determine. The following five difficulties are 
likely to arise : I. The cause may be out of 
our experience, and is therefore not to be un- 
derstood; 11. Causes often act conjointly, 
so that it is difficult to discover the one pre- 
dominant cause by reason of its associated 
causes ; III. Often the presence of a counter- 
acting, or modifying cause may confuse us; 
IV. Often a certain effect may be caused by 
either of several possible causes; V. That 
which appears as a cause of a certain effect 
may be but a co-effect of an original cause. 

Mill formulated several tests for ascertain- 
ing the causal agency in particular cases, in 
view of the above-stated difficulties. These 
tests are as follows: (1) The Method of 
Agreement; (2) The Method of Difference; 
(3) The Method of Eesidues; and (4) the 
Method of Concomitant Variations. The fol- 
lowing definitions of these various tests are 
given by Atwater as follows : 



Theoby and Hypotheses 129 

Method of Agreement: ^^If, whenever a 
given object or agency is present without 
counteracting forces, a given effect is pro- 
duced, there is a strong evidence that the ob- 
ject or agency is the cause of the effect." 

Method of Difference: "li, when the sup- 
posed cause is present the effect is present, 
and when the supposed cause is absent the 
effect is wanting, there being in neither case 
any other agents present to effect the result, 
we may reasonably infer that the supposed 
cause is the real one." 

Method of Residue : ^^ When in any phenom- 
ena we find a result remaining after the 
effects of all known causes are estimated, we 
may attribute it to a residual agent not yet 
reckoned. ' ' 

Method of Concomitant Variations : ^ ^ When 
a variation in a given antecedent is accom- 
panied by a variation of a given consequent, 
they are in some mianner related as cause and 
effect." 

Atwater adds: ^^ Whenever either of these 
criteria is found free from conflicting evi- 
dence, and especially when several of them 
concur, the evidence is clear that the cases ob- 



130 Logical Thinking 

served are fair representatives of the whole 
class, and warrant a valid inductive conclu- 
sion/^ 

Jevons gives us the following valuable 
rules: 

L ^^ Whenever we can alter the quantity of 
the things experimented on, we can apply a 
rule for discovering which are causes and 
which are effects, as follows : We must vary 
the quantity of one thing, making it at one 
time greater and at another time less, and if 
we observe any other thing which varies just 
at the same times, it will in all probability be 
an effect. ' ' 

II. ^^ When things vary regularly and fre- 
quently, there is a simple rule, by following 
which we can judge whether changes are con- 
nected together as causes and effects, as fol- 
lows : Those things which change in exactly 
equal times are in all likelihood connected to- 
gether/' 

III. ^^It is very difficult to explain how it is 
that we can ever reason from one thing to a 
class of things by generalization, when we 
ccmnot he sure that the things resemble each 
other in the important points. . . . Upon 



Theory and Hypotheses 131 

what grounds do we argue ? We have to get 
a general law from particular facts. This 
can only be done by going through all the 
steps of inductive reasoning. Having made 
certain observations, we must frame hypothe- 
ses as to the circumstances, or laws from 
which they proceed. Then we must reason 
deductively; and after verifying the deduc- 
tions in as many cases as possible, we shall 
know how far we can trust similar deductions 
concerning future events. ... It is diffi- 
cult to judge when we may, and when we may 
not, safely infer from some things to others 
in this simple way, without making a complete 
theory of the matter. The only rule that can 
be given to assist us is that if things resemble 
each other in a few properties only, we must 
observe many insta/nces before inferring that 
these properties will always be joined to- 
gether in other cases.' ^ 



CHAPTER XIV. 

MAKING AND TESTING HYPOTHESES 

The older philosopliers and logicians were 
often at a loss how to reasonably account for 
the origin of hypotheses. It will be seen, after 
giving the matter a little thought, that the 
actual formation of the hypothesis is more 
than a mere grouping together or synthesis 
of facts or ideas— there is another mental 
process which actually evolves the hypothesis 
or theory— which gives a possible reason. 
What is this mental process ? Let us consider 
the matter. Brooks well says : ' ' The hypoth- 
eses of science originate in what is called an- 
ticipation. They are not the result of a mere 
synthesis of facts, for no combination of facts 
can give the law or cause. We do not see the 
law ; we see the facts and the mind thinks the 
law. By the power of anticipation, the mind 
often leaps from a few facts to the cause which 
produces themi or the law which governs 
them. Many hypotheses were but a happy in- 
tuition of the mind. They were the result of 

132 



Testing Hypotheses 133 

what La Place calls ^a great guess,' or what 
Plato so beautifully designates as ^a sacred 
suspicion of truth/ The forming of hypoth- 
eses requires a suggestive mind, a lively fancy, 
a philosophic imagination, that catches a 
glimpse of the idea through the form, or sees 
the law standing behind the fact. ' ' 

The student of The New Psychology sees 
in the mental operation of the forming of the 
hypothesis— ^^ the mind thinking the law"— 
but an instance of the operation of the activi- 
ties of the Subconscious Mind, or even the 
Superconscious Mind. (See the volume on 
the Subconscious Mind in this series.) Not 
only does this hypothesis give the explanation 
which the old psychology has failed to do, 
but it agrees with the ideas of others on the 
subject as stated in the above quotation from 
Brooks ; and moreover agrees with many re- 
corded instances of the formation of great 
hypotheses. Sir Wmf. Hamilton discovered 
the very important mathematical law of qua- 
ternions while walking one day in the Dublin 
Observatory. He had pondered long on the 
subject, but without result. But, finally, on 
that eventful day he suddenly ^^felt the gal- 



134 Logical Thinking 

vanic circle of thought" close, and the result 
was the realization of the fundamental mathe- 
matical relations of the problem. Berthelot, 
the founder of Synthetic Chemistry, has testi- 
fied that the celebrated experiments which led 
to his remarkable discoveries were seldom 
the result of carefully followed lines of con- 
scious thought or pure reasoning processes; 
but, instead, came to him ^^of their own ac- 
cord,'^ so to speak, ^^as from a clear sky.'^ 
In these and many other similar instances, 
the mental operation was undoubtedly purely 
subjective and subconscious. Dr. Hudson 
has claimed that the ^^ Subjective Mind" can- 
not reason inductively, and that its opera- 
tions are purely and distinctly deductive, but 
the testimony of many eminent scientists, in- 
ventors and philosophers is directly to the 
contrary. 

In this connection the following quotation 
from Thomson is interesting: *^The system 
of anatomy which has immortalized the name 
of Oken is the consequence of a flash of an- 
ticipation which glanced through his mind 
when he picked up in a chance walk the skull 
of a deer, bleached and disintegrated by the 



Testing Hypotheses 135 

weather, and exclaimed after a glance, ^It is 
part of a vertebral colnnrn ! ' When Newton 
saw the apple fall, the anticipatory question 
flashed through his mind, ^Why do not the 
heavenly bodies fall like this apple ?^ In 
neither case had accident any important 
share; Newton and Oken were prepared by 
the deepest previous study to seize upon the 
unimportant fact odff ered to them, and to show 
how important it might become; and if the 
apple and the deer-skull had been wanting, 
some other falling body, or some other skull, 
would have touched the string so ready to 
vibrate. But in each case there was a great 
step of anticipation; Oken thought he saw a 
type of the whole skeleton in a single verte- 
bra, while Newton conceived at once that the 
whole universe was full of bodies tending to 
fall. • . . The discovery of Groethe, which 
did for the vegetable kingdom what Oken did 
for the animal, that the parts of a plant are 
to be regarded as metamorphosed leaves, is 
an apparent exception to the necessity of 
disciple for invention^ since it was the dis- 
covery of a poet in a region to which he 
seemed to have paid no especial or laborious 



136 Logical Thinkikg 

attention. But Goethe was himself most anx- 
ious to rest the basis of this discovery upon 
his observation rather than his imagination, 
and doubtless with good reason. ... As 
with other great discoveries, hints had been 
given already, though not pursued, both of 
Goethe's and Oken's principles. Goethe left 
his to be followed up by others, and but for his 
great fame, perhaps his name would never 
have been connected with it. Oken had 
amassed all the materials necessary for the 
establishment of his theory; he was able at 
once to discover and conquer the new terri- 
tory.'' 

It must not be supposed, however, that all 
hypotheses flashing into the field of conscious- 
ness from the Subconsciousness, are neces- 
sarily true or correct. On the contrary many 
of them are incorrect, or at least only partially 
correct. The Subconsciousness is not infal- 
lible or omniscient— it merely produces re- 
sults according to the material furnished it. 
But even these faulty hypotheses are often of 
value in the later formation of a correct one. 
As "Whewell says: ^^To try wrong guesses 
is with miost persons the only way to hit upon 



Testing Hypotheses 137 

right ones." Kepler is said to have erected 
at least twenty hypotheses regarding the 
shape of the earth's orbit before he finally 
evolved the correct one. As Brooks says: 
^ ' Even incorrect hypotheses may be of use in 
scientific research, since they may lead to 
more correct suppositions. The supposition 
of the circular motions of the heavenly bodies 
around the earth as a center, which lead to 
the conception of epicycles, etc., and at last to 
the true theory is an illustration of this. So 
the ^theory of phlogiston' in chemistry, made 
many facts intelligible, before the true one of 
^oxidation' superseded it. And so, as Thom- 
son says, ^^with the theory that ^Nature ab- 
hors a vacuum,' which served to bring to- 
gether so many cognate facts not previously 
considered as related. Even an incorrect 
conception of this kind has its place in science, 
so long as it is applicable to the facts; when 
facts occur which it cannot explain, we either 
correct it or replace it with a new one. The 
pathway of science, some one remarks, is 
strewn with the remains of discarded hypoth- 
eses." 
Halleck says regarding the danger of hasty 



138 Logical Thinking 

infereiice: ^^Men moist constantly employ im- 
perfect induction in order to advance ; but 
great dangers attend inductive inferences 
made from too narrow experience. A child 
has experience with one or two dogs at his 
home. Because of their gentleness, he argues 
that all dogs are gentle. He does not, per- 
haps, find out the contrary until he has been 
severely bitten. His induction was too hasty. 
He had not tested a sufficiently large number 
of dogs to form such a conclusion. From one 
or two experiences with a large crop in a cer- 
tain latitude, a farmer may argue that the 
crop will generally be profitable, whereas it 
may not again prove so for years. A man 
may have trusted a number of people and 
found them honest. He concludes that people 
as a rule are honest, trusts a certain dishon- 
est man, and is ruined. The older people 
grow, the more cautious they generally be- 
come in forming inductive conclusions. Many 
instances are noted and compared; but even 
the wisest sometimes make mistakes. It once 
was a generally accepted fact that all swans 
were white. Nobody had ever seen a dark 
swan, and the inference that all swans were 



Testing Hypotheses 139 

white was regarded as certainly true. Black 
swans were, however, found in Australia.'' 

Brooks says regarding the probability of 
hypotheses: ^^The probability of a hypoth- 
esis is in proportion to the number of facts 
and phenomena it will explain. The larger 
the number of facts and phenomena that it 
will satisfactorily account for, the greater our 
faith in the correctness of our supposition. 
... If there is more than one hypoth- 
esis in respect to the facts under considera- 
tion, that one which accounts for the greatest 
number of facts is the most probable. 
. . . In order to verify a hypothesis it 
must be shown that it will account for all the 
facts and phenomiena. If these facts are 
numerous and varied, and the subject is so 
thoroughly investigated that it is quite cer- 
tain that no important class of facts has been 
overlooked, the supposition is regarded as 
true, and the hypothesis is said to be verified. 
Thus the hypothesis of the ^ daily rotation' of 
the earth on its axis to account for the succes- 
sion of day and night is accepted as absolutely 
true. This is the view taken by Dr. Whewell 
and many other thinkers in respect to the 



140 Logical Thinking 

verification of a hypothesis. Some writers, 
however, as Mill and his school, maintain that 
in order to verify a hypothesis, we must show 
not only that it explains all the facts and 
phenomena, but that there is no other possi- 
ble hypothesis which will account for them. 
. . . The former view of verification is 
regarded as the correct one. By the latter 
view, it is evident that a hypothesis could 
never be verified. ' ' 

Jevons says: '^In the fourth step (verifica- 
tion), we proceed to compare these deductions 
with the facts already collected, or when nec- 
essary and practicable, we make new obser- 
vations and plan new experiments, so as to 
find out whether the hypothesis agrees with 
nature. If we meet with several distinct dis- 
agreements between our deductions and our 
observations, it will become likely that the 
hypothesis is wrong, and we must then invent 
a new one. In order to produce agreement it 
will sometimes be enough to change the hy- 
pothesis in a small degree. When we get hold 
of a hypothesis which seems to give results 
agreeing with a few facts, we must not at 
once assume that it is certainly correct We 



Testiitg Hypotheses 141 

must go on making other deductions from it 
under various circumstances, and, whenever 
it is possible, we ought to verify these re- 
sults, that is, compare them with facts ob- 
served through the senses. When a hypothe- 
sis is shown in this way to be true in a great 
many of its results, especially when it en- 
ables us to predict what we should never 
otherwise have believed or discovered, it be- 
comes certain that the hypothesis itself is a 
true one. . . . Sometimes it will happen 
that two or even three quite different hypothe- 
ses all seem to agree with certain facts, so that 
we are puzzled which to select. . . . When 
there are thus two hypotheses, one as good as 
the other, we need to discover some fact or 
thing which will agree with one hypothesis 
and not with the other, because this imme- 
diately enables us to decide that the former 
hypothesis is true and the latter false." 

In the above statements regarding the 
verification of hypotheses we see references 
made to the testing of the latter upon the 
'^ facts" of the case. These facts may be 
either the observed phenomena or facts appar- 
ent to the perception, or else facts obtained 



142 Logical Thinking 

by deductive reasoning. The latter may be 
said to be facts which are held to be true if the 
hypothesis be true. Thus if we erect the hy- 
pothesis that ^^AU men are mortal/' we may 
reason deductively that it will follow that 
each and every thing that is a man must die 
sooner or later. Then we test our hypotheses 
upon each and every man whom we may sub- 
ject to observation and experiment. If we 
find a single man who does not die, then the 
test disproves our hypotheses ; if on the con- 
trary all men (the ^^ facts'' in the case) prove 
to be mortal, then is our hypotheses proven or 
established. The deductive reasoning in this 
case is as follows: ''If so-and-so is true re- 
garding such-and-such a class ; and if this 
particular thing belongs to that class ; then it 
will follow that so-and-so is true regarding 
this particular thing." This argument is ex- 
pressed in what is called a Hypothetical 
Proposition (see Chapter IX), the considera- 
tion of which forms a part of the general sub- 
ject of Deductive Eeasoning. Therefore as 
Jevons has said, '^Deductive Reasoning is the 
Third Step in Inductive Reasoning, and pre- 
cedes Verification", which we have already 



Testing Hypotheses 143 

considered. Halleck says: ^^ After Induction 
has classified certain phenomena and thus 
given us a major premise, we may proceed 
deductively to apply the inference to any new 
specimen that can be shown to belong to that 
class. Induction hands over to deduction a 
ready-made major premise. . . . Deduc- 
tion takes that as a fact, making no inquiry 
about its truth. . . . Only after general 
laws have been laid down, after objects have 
been classified, after major premises have 
been formed, can deduction be employed. ^^ 

In view of the above facts, we shall now 
proceed to a consideration of that great class 
of Reasoning known under the term— Deduc- 
tive Reasoning. 



CHAPTER XV. 

DEDUCTIVE EEASONING 

We have seen that there are two great 
classes of reasoning, known respectively, as 
(1) Inductive Reasoning, or the discovery of 
general truth from particular truths ; and (2) 
Deductive Reasoning, or the discovery of par- 
ticular truths from general truths. 

As we have said. Deductive Reasoning is 
the process of discovering particular truths 
from a general truth. Thus from the gen- 
eral truth embodied in the proposition ^^All 
horses are animals,'' when it is considered in 
connection with the secondary proposition 
that ^^ Dobbin is a horse,'' we are able to de- 
duce the particular truth that: ^^ Dobbin is 
an animal." Or, in the following case we 
deduce a particular truth from a general 
truth, as follows: ^^All mushrooms are good 
to eat ; this fungus is a mushroom ; therefore, 
this fungus is good to eat. ' ' A deductive argu- 
ment is expressed in a deductive syllogism. 

Jevons says regarding the last stated il- 

144 



Deductive Eeasoning 145 

lustration: ''Here are three sentences which 
state three different facts; but when we 
know the two first facts, we learn or gather 
the third fact from the other two. When 
we thus learn one fact from other facts, we 
infer or reason, and we do this in the mind. 
Seasoning thus enables us to ascertain the 
nature of a thing without actual trial. If we 
always needed to taste a thing before we could 
know whether it was good to eat or not, cases 
of poisoning would be alarmingly frequent. 
But the appearance and peculiarities of a 
mushroom may be safely learned by the eye 
or the nose, and reasoning upon this informa- 
tion and the fact already well known, that 
mushrooms are good to eat, we arrive with- 
out any danger or trouble at the conclusion 
that the particular fungus before us is good 
to eat. To reason, then, is to get some knowl- 
edge from other knowledge.^ ^ 

The student will recognize that Deductive 
Eeasoning is essentially an analytic process, 
because it operates in the direction of analyz- 
ing a universal or general truth into its par- 
ticulars—into the particular parts which are 
included within it— and asserting of them that 



146 Logical Thinking 

**what is true of the general is true of the 
particnlar.'^ Thus in the general truth that 
**A11 men are mortal/^ we see included the 
particular truth that *^ John Smith is mortaP' 
—John Smith having been discovered to be a 
man. We deduce the particular truth about 
John Smith from the general truth about ^*all 
men. ^ * We analyze * ^ all men ' ' and find John 
Smith to be one of its particular parts. 
Therefore, *^ Deduction is an inference from 
the whole to its parts; that is, an analytic 
process. '^ 

The student will also recognize that Deduc- 
tive Eeasoning is essentially a\ descending 
process, because it operates in the direction of 
a descent from the universal to the particu- 
lar; from the higher to the lower; fronn the 
broader to the narrower. As Brooks says: 
^* Deduction descends from higher truths to 
lower truths, from laws to facts, from causes 
to phenomena, etc. Given the law, we can 
by deduction descend to the facts that fall 
under the law, even if we have never before 
seen the facts ; and so from the cause we may 
pass down to observed and even unknown 
phenomena.'' 



Deductive Reasoning 147 

The general truths which are used as the 
basis of Deductive Reasoning are discovered 
in several ways. The majority arise from In- 
ductive Reasoning, based upon experience, 
observation and experiment. For instance in 
the examples given above, we could not truth- 
fully assert our belief that: ^^AU horses are 
animals'' unless we had previously studied 
both the horse and animals in general. Nor 
without this study could we state that ^^ Dob- 
bin is a horse. '^ Nor could we, vdthout pre- 
vious study, experience and experiment truth- 
fully assert that: ^^AU miushrooms are good 
to eat;" or that *^this fungus is a mush- 
room;" and that ^ therefore, this fungus is 
good to eat. ' ' Even as it is, we must be sure 
that the fungus really is a mushroom, else we 
run a risk of poisoning ourselves. General 
truths of this kind are not intuitive, by any 
means, but are based upon our own experi- 
ence or the experience of others. 

There is a class of general truths which are 
called intuitive by some authorities. Halleck 
says of these: ^^Some psychologists claim 
that we have knowledge obtained neither 
through induction nor deduction; that we 



148 Logical Thinking 

recognize certain truths the moment we per- 
ceive certain objects, without any process of 
inference. Under the head of intuitive knowl- 
edge are classified such cases as the follow- 
ing: We perceive an object and immediately 
know that it is a time relation, as existing now 
and then. We are said to have an intuitive 
concept of time. When we are told that the 
whole is greater than a part ; that things equal 
to the same thing are equal to each other ; that 
a straight line cannot enclose space, we imme- 
diately, or intuitively, recognize the truth of 
these statements. Attempts at proof do not 
make us feel surer of their truth. . . . 
We say that it is self-evident, or that we know 
the fact intuitively. The axioms of mathe- 
matics and logic are said to be intuitive.'' 

Another class of authorities, however, deny 
the nature of intuitive knowledge of truth, or 
intuitive truths. They claun that all our ideas 
arise from sensation and reflection, and that 
what we call ^ intuition" is merely the result 
of sensation and reflection reproduced by 
memory or heredity. They hold that the in- 
tuitions of animals and men are simply the 
representation of experiences of the race, or 



Deductive Reasoning 149 

individual, arising from the impressions 
stored away in the subconsciousness of the 
individual. Halleck states regarding this: 
^^This school likens intuition to instinct. It 
grants that the young duck knows water in- 
stinctively, plunges into it, and swims without 
learning. These psychologists believe that 
there was a time when this was not the case 
with the progenitors of the duck. They had 
to gain this knowledge slowly through ex- 
perience. Those that learned the proper 
aquatic lesson survived and transmitted this 
knowledge through a modified structure, to 
their progeny. Those that failed in the les- 
son perished in the struggle for existence. 
. . . This school claims that the in/tui- 
tion of cause and effect arose in the same way. 
Generations of human beings have seen the 
cause invariably joined to the effect; hence, 
through inseparable association came the 
recognition of their necessary sequence. The 
tendency to regard all phenomena in these 
relations was with steadily increasing force 
transmitted by the laws of heredity to pos- 
terity, until the recognition of the relation- 
ship has become an intuition. ^^ 



150 Logical Thinking 

Another class of general truths is merely 
hypothetical. Hypothetical means *^ Found- 
ed on or including a hypothesis or supposi- 
tion; assumed or taken for granted, though 
not proved, for the purpose of deducing 
proofs of a point in question.'^ The hypothe- 
ses and theories of physical science are used 
as general truths for deductive reasoning. 
Hypothetical general truths are in the nature 
of premises assumed in order to proceed with 
the process of Deductive Eeasoning, and 
without which such reasoning would be im- 
possible. They are, however, as a rule not 
mere assumptions, but are rather in the na- 
ture of assumptions rendered plausible by 
experience, experiment and Inductive Eeason- 
ing. The Law of Gravitation may be con- 
sidered hypothetical, and yet it is the result 
of Inductive Eeasoning based upon a vast 
multitude of facts and phenomena. 

The Primary Basis of Dedv^ctive Reasoning 
may be said to rest upon the logical axiom, 
which has come down to us from the ancients, 
and which is stated as follows: ^^ Whatever 
is true of the whole is true of its parts/ ^ Or, 
as later authorities have expressed it: ^* What- 



Deductive Eeasoning 151 

ever is true of the general is true of the par- 
ticular.'? This axiom is the basis upon which 
we build our Deductive Reasoning. It fur- 
nishes us with the validity of the deductive 
inference or argument. If we are challenged 
for proof of the statement that ' ' This fungus 
is good to eat/' we are able to answer that 
we are justified in making the statement by 
the self-evident proposition, or axiom, that 
^* Whatever is true of the general is true of 
the particular. ' ' If the general ' ^ mushroom ' ' 
is good to eat, then the particular, ^^this fun- 
gus'' being a mushroom, must also be good to 
eat. All horses (general) being animals, 
then according to the axiom, Dobbin (partic- 
ular horse) must also be an animal. 

This axiom has been stated in various terms 
other than those stated above. For instance : 
'^Whatever may be affirmed or denied of the 
whole, may be denied or affirmed of the 
parts;'* which form is evidently derived 
from that used by Hamilton who said : ^ * What 
belongs, or does not belong, to the containing 
whole, belongs or does not belong, to each of 
the contained parts." Aristotle formulated 
his celebrated Dictum as follows: ''What- 



152 Logical Thinking 

ever can be predicated affirmatively or nega- 
tively of any class or term distributed, can be 
predicated in like manner of all and singular 
the classes or individuals contained under it.'^ 

There is another form of Deductive Eea- 
soning, that is a form based upon another ax- 
iom than that of: ^^ Whatever is true of the 
whole is true of the parts. '^ This form of 
reasoning is sometimes called Mathematical 
Eeasoning, because it is the form of reasoning 
employed in mathematics. Its axiom is 
stated as follows: *^ Things which are equal 
to the same thing, are equal to one another/' 
It will be seen that this is the principle em- 
ployed in mathematics. Thus: ^^x equals y; 
and y equals 5; therefore, x equals 5.^' Or 
stated in logical terms: ^^A equals B; B 
equals C; therefore, A equals C' Thus it is 
seen that this form of reasoning, as well as 
the ordinary form of Deductive Eeasoning, is 
strictly mediate, that is, made through the 
medium of a third thing, or ' ' two things being 
compared through their relation to a third.'' 

Brooks states: "The real reason for the 
certainty of mathematical reasoning may be 
stated as follows: First, its ideas are defi- 



Deductive Reasoning 153 

nite, necessary, and exact conceptions of 
quantity. Second, its definitions, as the de- 
scription of these ideas are necessary, exact, 
and indisputable truths. Third, the axioms 
from which we derive conclusions by compari- 
son are all self-evident and necessary truths. 
Comparing these exact ideas by the necessary 
laws of inference, the result must be abso- 
lutely true. Or, stated in another way, using 
these definitions and axioms as the premises 
of a syllogism, the conclusion follows inevi- 
tably. There is no place or opportunity for 
error to creep in to mar or vitiate our derived 
truths. '^ 

In conclusion, we wish to call your atten- 
tion ' to a passage from Jevons which is 
worthy of consideration and recollection. 
Jevons says : ' ^ There is a simple rule which 
will enable us to test the truth of a great many 
arguments, even of many which do not come 
under any of the rules commonly given in 
books on logic. This rule is that whatever is 
true of one term is true of any term which is 
stated to he the same in meaning as that term. 
In other words, we may always substitute one 
term for another if we know that they refer to 



154 Logical Thinking 

exactly the same thing. There is no doubt 
that a horse is some animal, and therefore the 
head of a horse is the head of some animal. 
This argmnent cannot be brought under the 
rules of the syllogism, because it contains 
four distinct logical terms in two proposi- 
tions; namely, horse, some animal; head of 
horse, head of some animal. But it easily 
comes under the rule which I have given, be- 
cause we have simply to put ' some animal' in- 
stead of ^a horse'. A great many arguments 
may be explained in this way. Gold is a 
metal ; therefore a piece of gold is a piece of 
metal. A negro is a fellow creature; there- 
fore, he who strikes a negro, strikes a fellow 
creature." 

The same eminent authority says: ^^When 
we examine carefully enough the way in which 
we reason, it will be found in every case to 
consist in putting one thing or term in place of 
another, to which we know it to have an exact 
resemblance in some respect. We use the 
likeness as a kind of bridge, which leads us 
from a knowledge of one thing to a knowledge 
of another ; thus the true principle of reason- 
ing may he called the substitution of similars, 



Deductive Reasoning 155 

or the passing from like to like. We infer the 
character of one thing from the character of 
something which acts as a go-between, or 
third term. When we are certain there is an 
exact likeness, our inference is certain; when 
we only believe that there probably is, or 
guess that there is, then our inferences are 
only probable, not certain/^ 



CHAPTEE XVI. 

THE SYLLOGISM 

The third and highest phase or step in 
reasoning— the step which follows after those 
styled Conception and Judgment— is gener- 
ally known by the general term ^ ' Reasoning, ' ' 
which term, however, is used to include the 
two precedent steps as well as the final step 
itself. This step or process consists of the 
comparing of two objects, persons or things, 
through their relation to a third object, per- 
son or thing. As, for instance, we reason (a) 
that all mammals are animals; (b) that a 
horse is a mammal; and (c) that, therefore, a 
horse is an animal. The most fundamental 
principle of this step or reasoning consists in 
the comparing of two objects of thought 
through and by means of their relation to a 
third object. The natural form of expression 
of this process of reasoning is called a ^* Syllo- 
gism. '^ 

The process of reasoning which gives rise 
to the expression of the argument in the form 

156 



The Syllogism 157 

of a Syllogism must be understood if one 
wishes to form a clear conception of the Syllo- 
gism. The process itself is very simple when 
plainly stated, although the beginner is some- 
times puzzled by the complicated definitions 
and statements of the authorities. Let us sup- 
pose that we have three objects, A, B and C, 
respectively. We wish to compare C and B, 
but fail to establish a relation between them 
at first. We however are able to establish a 
relation between A and B ; and between C and 

A. We thus have the two propositions (1) 
^^A equals B; and (2) C equals A'\ The 
next step is that of inferring that ' ^ if A equals 

B, and C equals A, then it must follow, logic- 
ally, that C equals B/^ This process is that 
of indirect or mediate comparison, rather 
than immediate. C and B are not compared 
directly or immediately, but indirectly and 
through the medium of A. A is thus said to 
mediate between B and C. 

This process of reasoning embraces three 
ideas or objects of thought, in their expres- 
sion of propositions. It comprises the funda- 
mental or elemental form of reasoning. As 
Brooks says : ^ ^ The simplest movement of the 



158 Logical Thinking 

reasoning process is the comparing of two 
objects through their relation to a third/* 
The result of this process is an argument ex- 
pressed in what is called a Syllogism. Whate- 
ly says that: *^A Syllogism is an argument 
expressed in strict logical form so that its 
conclusiveness is manifest from the structure 
of the expression alone, without any regard 
to the meaning of the terms/' Brooks says: 
**A11 reasoning can be and naturally is ex- 
pressed in the form of the syllogism. It ap- 
plies to both inductive and deductive reason- 
ing, and is the form in which these processes 
are presented. Its importance as an instru- 
mient of thought requires that it receive spe- 
cial notice.'* 

In order that the nature and use of the 
Syllogism may be clearly understood, we can 
do no better than to at once present for your 
consideration the well-known ^^Kules of the 
Syllogism,'' an understanding of which 
carries with it a perfect comprehension of the 
Syllogism itself. 

The Eules of the Syllogism state that in 
order for a Syllogism to be a perfect Syllo- 
gism, it is necessary : 



The Syllogism 159 

I. That there should be three, and no more 
than three, Propositions. These three prop- 
ositions are: (1) the Conclusion, or thing to 
be proved; and (2 and 3) the Premises, or the 
means of proving the Conclusion, and which 
are called the Major Premise and Minor Pre- 
mise, respectively. We may understand this 
more clearly if we will examdne the following 
example : 

Major Premise: ^^Man is mortal; (or ^^A 

isB^O- 
Minor Premise : ^ ^ Socrates is a man ; " (or 

^^CisA'O. Therefore: 

Conclusion: ^^ Socrates is mortal" (or **C 
isB'O 

It will be seen that the above Syllogism, 
whether expressed in words or symbols, is 
logically valid, because the conclusion must 
logically follow the premises. And, in this 
case, the premises being true, it must follow 
that the conclusion is true. Whately says: 
* ' A Syllogism is said to be valid when the con- 
clusion logically follows from the premises; 
if the conclusion does not so follow, the Syllo- 
gism is invalid and constitutes a Fallacy, if 
the error deceives the reasoner himself; but 



160 Logical Thinking 

if it is advanced with the idea of deceiving 
others it constitutes a Sophism/^ 

The reason for Eule I is that only three 
propositions— a Major Premise, a Minor 
Premise, and a Conclusion— are needed to 
form a Syllogism, If we have more than 
three propositions, then we must have more 
than two premises from which to draw one 
conclusion. The presence of more than two 
premises would result in the formation of 
two or more Syllogisms, or else in the failure 
to form a Syllogism. 

II. That there should be three and no more 
than three Terms. These Terms are (1) The 
Predicate of the Conclusion; (2) the Subject 
of the Conclusion; and (3) the Middle Term 
which must occur in both premises, being the 
connecting link in bringing the two other 
Terms together in the Conclusion. 

The Predicate of the Conclusion is called 
the Major Term, because it is the greatest in 
extension compared with its fellow terms. 
The Subject of the Conclusion is called the 
Minor Term because it is the smallest in ex- 
tension compared with its fellow terms. The 
Major and Minor Terms are called the Eoo- 



The Syllogism 161 

tremes. The Middle Term operates between 
the two Extremes. 

The Major Term and the Middle Term must 
appear in the Major Premise. 

The Minor Term and the Middle Term must 
appear in the Minor Premise. 

The Minor Term and the Major Term must 
appear in the Conclusion. 

Thus we see that The Major Term must be 
the Predicate of the Conclusion; the Minor 
Term the Subject of the Conclusion; the Mid- 
dle Term may be the Subject or Predicate of 
either of the premises, but must always be 
found once in both premises. 

The following example will show this ar- 
rangement more clearly : 

In the Syllogism: *^Man is mortal; Socra- 
tes is a man; therefore Socrates is mortal," 
we have the following arrangement: ^^ Mor- 
tal," the Major Term; ^^ Socrates," the 
Minor Term; and ''Man," the Middle Term; 
as follows : 

Major Premise: ^^Man" {middle term) is 
mortal (major term). 

Minor Premise: ''Socrates" {minor term) 
is a man {major term). 



^^ 



162,, Logical Thinking 

Conclusion: ^^ Socrates" (minor term) is 
mortal (major term). [ 

Tke reason for the rule that there shall be 
*^only three^^ terms is that reasoning consists 
in comparing two terms with each other 
through the medium of a third term. There 
must he three terms; if there are more than 
three terms, we form two syllogisms instead 
of one. 

III. That one premise, at least, must he 
affirmative. This, because ^'from two nega- 
tive propositions nothing can be inferred." 
A negative proposition asserts that two things 
differ, and if we have two propositions so as- 
serting difference, we can infer nothing from 
them. If our Syllogism stated that: (1) 
**Man is not mortal;" and (2) that *^ Socra- 
tes is not a man;" we could formi no Conclu- 
sion, either that Socrates was or was not mor- 
tal. There would be no logical connection 
between the two premises, and therefore no 
Conclusion could be deduced therefrom. 
Therefore, at least one premise must be af- 
firmative. 

IV. If one premise is negative, the conclu- 
sion must he negative. This because ^^if one 



The Syllogism 163 

term agrees and another disagrees with a 
third term, they must disagree with each 
other/' Thus if our Syllogism stated that: 
(1) ^^Manisw^ mortal; "and (2) that:^^Soc- 
rates is a man;'' we must announce the Nega- 
tive Conclusion that: (3) *^ Socrates is not 
mortal." 

V. That the Middle Term must he distrib- 
uted; (that is, taken universally) in at least 
one premise. This ^* because, otherwise, the 
Major Term may be compared with one part 
of the Middle Term, and the Minor Term with 
another part of the latter ; and there will be 
actually no coromon Middle Term, and conse- 
quently no common ground for an inference. ' ' 
The violation of this rule causes what is com- 
monly known as ^^The Undistributed Mid- 
dle," a celebrated Fallacy condemned by the 
logicians. In the Syllogism mentioned as an 
example in this chapter, the proposition ^^Man 
is mortal," really means '^ All men," that is, 
Man in his universal sense. Literally the prop- 
osition is ^^ Air men are mortal," from which 
it is seen that Socrates being '^a man" (or 
some of all men) must partake of the quality 
of the universal Man. If the Syllogism, in- 



1 

164 Logical Thi^s-king 

stead, read: ''Some' men are mortal," it 
woiild not follow that Socrates must be mortal 
— fre might or might not be so. Another form 
of this fallacy is shown in the statement that 
(1) "White is a color; (2) Black is a color; 
hence (3) Black must be White. The two pre- 
mises really mean ^^ White is some color; 
Black is some color; and not that either is 
' ' all colors. ' ' Another example is : ^ ^ Men are 
bipeds; birds are bipeds; hence, men are 
birds.'' In this example ^^ bipeds'' is not dis- 
tributed as "all bipeds" but is simply not-dis- 
tributed as "some bipeds." These syllo- 
gisms, therefore, not being according to rule, 
must fail. They are not true syllogisms, and 
constitute fallacies. 

To be "distributed^^' the Middle Term must 
be the Subject of a Universal Proposition, or 
the Predicate of a Negative Proposition; to 
be " undistributed' ' it must be the Subject of 
a Particular Proposition, or the Predicate of 
an Affirmative Proposition. (See chapter on 
Propositions.) 

VI. That an extreme, if undistributed in a 
Premise, may not be distributed in the Con- 
clusion. This because it would be illogical and 



The Syllogism 165 

unreasonable to assert more in the conclusion 
than we find in the premises. It would be 
most illogical to argue that: (1) ^^AU horses 
are animals; (2) no man is a horse; there- 
fore (3) no man is an animal. '^ The conclu- 
s.ion would be invalid, because the term ani- 
mal is distributed in the conclusion, (being 
the predicate of a negative proposition) while 
it is not distributed in the premise (being the 
predicate of an affirmative proposition). 

As we have said before, any Syllogism 
which violates any of the above six syllogisms 
is invalid and a fallacy. 

There are two additional rules which may 
be called derivative. Any syllogism which 
violates either of these two derivative rules, 
also violates one or more of the first six rules 
as given above in detail. 

The Two Derivative Rules of the Syllogism 
are as follows : 

Vn. That one Premise at least must he 
Universal. This because ^^from two particu- 
lar premises no conclusion can be drawn.'' 

VIII. That if one premise is Particular, the 
Conclusion must he particular also. This be- 



166 Logical Thinking 

cause only a universal conclusion can be 
drawn from two universal premises. 

The principles involved in these two Deri- 
vative Eules may be tested by stating Syllo- 
gisms violating them. They contain the es- 
sence of the other rules, and every syllogism 
which breaks them will be found to also break 
one or more of the other rules given. 



CHAPTEE XVII. 

VARIETIES OF SYLLOGISMS 

The authorities in Logic hold that with the 
four kinds of propositions grouped in every 
possible order of arrangement, it is possible 
to form nineteen different kinds of valid argu- 
ments, which are called the nineteen moods 
of the syllogism. These are classified by di- 
vision into what are called the four figures, 
each of which figures may be known by the po- 
sition of the middle term in the premises. Lo- 
gicians have arranged elaborate and curious 
tables constructed to show what kinds of prop- 
ositions when joined in a particular order of 
arrangement will make sound and valid syllo- 
gisms. We shall not set forth these tables 
here, as they are too technical for a popular 
presentation of the subject before us, and be- 
cause they are not necessary to the student 
who will thoroughly familiarize himself with 
the above stated Laws of the Syllogism and 
who will therefore be able to determine in 

167 



168 Logical Thinking 

every case whether any given argument is a 
correct syllogism, or otherwise. 

In many instances of ordinary thought and 
expression the complete syllogistic form is 
omitted, or not stated at full length. It is com- 
mon usage to omit one premise of a syllogism, 
in ordinary expression, the missing premise 
being inferred by the speaker and hearer. A 
syllogism with one premise unexpressed is 
sometimes called an Enthymene, the term 
meaning ^4n the mind.'' For instance, the 
following: *^We are a free people, therefore 
we are happy," the major premise ^^All free 
people are happy'' being omitted or unex- 
pressed. Also in ^^ Poets are imaginative, 
therefore Byron was imaginative," the minor 
premise ^ ' Byron was a poet ' ' is omitted or un- 
expressed. Jevons says regarding this phase 
of the subject : ^ ' Thus in the Sermon on the 
Mount, the verses known as the Beatitudes 
consist each of one premise and a conclusion, 
and the conclusion is put first. ^Blessed are 
the merciful: for they shall obtain mercy.' 
The subject and the predicate of the conclu- 
sion are here inverted, so that the proposition 
is really ^ The merciful are blessed. ' It is ev- 



Varieties of Syllogisms 169 

idently understood that ^AU who shall obtain 
mercy are blessed, ' so that the syllogism, when 
stated at full length, becomes: ^All who shall 
obtain mercy are blessed ; All who are merci- 
ful shall obtain mercy ; Therefore, all who are 
merciful are blessed/ This is a perfectly 
good syllogism." 

Whenever we find any of the words: ^^fee- 
cause^ for, therefore, since/' or similar terms, 
we may know that there is an argument, and 
usually a syllogism. 

We have seen that there are three special 
kinds of Propositions, namely, (1) Categori- 
cal Propositions, or propositions in which the 
affirmation or denial is made without reser- 
vation or qualification; (2) Hypothetical 
Propositions, in which the affirmation or de- 
nial is made to depend upon certain condi- 
tions, circumstances, or suppositions; and (3) 
Disjunctive Propositions, in which is im- 
plied or asserted an alternative. 

The forms of reasoning based upon these 
three several classes of propositions bear the 
same names as the latter. And, accordingly 
the respective syllogisms expressing these 
forms of reasoning also bear the class name or 



170 Logical Thinking 

term. Tlras, a Categorical Syllogism is one 
containing only categorical propositions; a 
Hypothetical Syllogism is one containing one 
or more hypothetical propositions ; a Disjunc- 
tive Syllogismi is one containing a disjunctive 
proposition in the major premise. 

Categorical Syllogisms, which are far more 
common than the other two kinds, have been 
considered in the previous chapter, and the 
majority of the examples of syllogisms given 
in this book are of this kind. In a Categorical 
Syllogism the statement or denial is made pos- 
itively, and without reservation or qualifica- 
tion, and the reasoning thereupon partakes of 
the same positive character. In propositions 
or syllogisms of this kind it is asserted or as- 
sumed that the premise is true and correct, 
and, if the reasoning be logically correct it 
must follow that the conclusion is correct, and 
the new proposition springing therefrom must 
likewise be Categorical in its nature. 

Hypothetical Syllogisms, on the contrary, 
have as one or more of their premises a hypo- 
thetical proposition which affirms or asserts 
something provided, or *4f," something else 
be true. Hyslop says of this : ' ' Often we wish 



Varieties of Syllogisms 171 

first to bring out, if only conditionally, the 
truth upon which a proposition rests, so as to 
see if the connection between this conclusion 
and the major premise be admitted. The whole 
question will then depend upon the matter of 
treating the minor premise. This has the ad- 
vantage of getting the major premise admit- 
ted without the formal procedure of proof, 
and the minor premise is usually more easily 
proved than the major. Consequently, one is 
made to see more clearly the force of the ar- 
gument or reasoning by removing the ques- 
tion of the material truth of the major premise 
and concentrating attention upon the relation 
between the conclusion and its conditions, so 
that we know clearly what we have first to 
deny if we do not wish to accept it. ' ' 

By joining a hypothetical proposition with 
an ordinary proposition we create a Hypo- 
thetical Proposition. For instance: ''// 
York contains a cathedral it is a city; York 
does contain a cathedral; therefore, York is a 
city.'' Or: ^^If dogs have four feet, they are 
quadrupeds; dogs do have four feet; there- 
fore dogs are quadrupeds." The Hypotheti- 
cal Syllogism may be either affirmative or 



172 Logical Thinking 

negative ; that is, its hypothetical proposition 
may either hypothetically affirm or hypothet- 
ieally deny. The part of the premise of a Hy- 
pothetical Syllogism which conditions or ques- 
tions (and which usually contains the little 
word * 4f ^ is called the Antecedent. The ma- 
jor premise is the one usually thus condition- 
ed. The other part of the conditioned propo- 
sition, and which part states what will happen 
or is true under the conditional circumstances, 
is called the Consequent. Thus, in one of the 
above examples : ^ * If dogs have four f eet ^ ' is 
the Antecedent; and the remainder of the 
proposition: *^they are quadrupeds'^ is the 
Consequent. The Antecedent is indicated by 
the presence of some conditional term as : if, 
supposing^ granted that, provided that, al- 
though, had, were, etc., the general sense and 
meaning of such terms being that of the little 
word '^i/.'' The Consequent has no special 
indicating term. 

Jevons gives the following clear and simple 
Rules regarding the Hypothetical Syllogism : 

I. * ^ If the Antecedent be aflSrmed, the con- 
sequent may be affirmed. If the Consequent 
be denied, the Antecedent may be denied.'* 



Varieties of Syllogisms ; 173 

IL ^^ Avoid the fallacy of afl&rming the 
consequent, or denying the antecedent. This 
is a fallacy because of the fact that the condi- 
tional statement made in the major premise 
may not he the only one determining the con- 
sequenf The following is an example of 
'^Affirming the Consequent:" ^'If it is rain- 
ing, the sky is overclouded; the sky is over- 
clouded; therefore, it is raining. '^ In truth, 
the sky may be overclouded, and still it may 
not be raining. The fallacy is still more ap- 
parent when expressed in symbols, as follows: 
''If A is B, C is D ; C i5 D ; therefore, A is B.'^ 
The fallacy of denying the Antecedent is 
shown by the following example: ''If Ea- 
dium were cheap it would be useful ; Radium 
is not cheap ; therefore Radium is not useful. ' ' 
Or, expressed in symbols : "If A. is B, C is D ; 
A is not B ; therefore C is not D." In truth 
Radium may be useful although n<5t cheap. 
Jevons gives the following examples of these 
fallacies: ^^If a man is a good teacher, he 
thoroughly understands his subject ; but John 
Jones thoroughly understands his subject; 
therefore, he is a good teacher." Also, ^^If 
snow is mixed with salt it melts ; the snow on 



174 Logical Thinking 

the ground is not mixed with salt; therefore 
it does not melt/' 

Jevons says: *^To affirm the consequent 
and then to infer that we can affirm the ante- 
cedent, is as bad as breaking the third rule of 
the syllogism, and allowing an undistributed 
middle term. . . . To deny the antece- 
dent is really to break the fourth rule of the 
syllogism, and to take a term as distributed in 
the conclusion which was not so in the pre- 
mises/' 

Hypothetical Syllogisms miay usually be 
easily reduced to or converted into Gategori- 
cal Syllogisms. As Jevons says : * * In reality, 
hypothetical propositions and syllogisms are 
not different from those which we have more 
fully considered. It is all a matter of the con- 
venience of stating the propositions.*^ For in- 
stance, instead of saying: *^If Eadium were 
cheap, it would be useful," we may say 
' ^ Cheap Radium would be useful ; " or instead 
of saying : ^ ' If glass is thin, it breaks easily, ' ' 
we may say ^^Thin glass breaks easily." Hy- 
slop gives the following Rule for Conversion 
in such cases : ^ * Regard the antecedent of the 
hypothetical proposition as the subject of the 



Varieties of Syllogisms 175 

categorical, and the consequent of the hypo- 
thetical proposition as the predicate of the 
categorical. In some cases this change is a 
very simple one; in others it can be effected 
only by a circumlocution. '' 

The third class of syllogisms, known as The 
Disjunctive 8yllogism\y is the exception to the 
law which holds that all good syllogisms must 
fit in and come under the Eules of the Syllo- 
gism, as stated in the preceding chapter. Not 
only does it refuse to obey these Eules, but it 
fails to resemble the ordinary syllogism in 
many ways. As Jevons says: ^^It would be 
a great mistake to suppose that all good logi- 
cal arguments must obey the rules of the syl- 
logism, which we have been considering. Only 
those arguments which connect two terms to- 
gether by means of a middle term;, and are 
therefore syllogisms, need obey these rules. 
A great many of the arguments which we 
daily use are of this nature ; but there are a 
great many other kinds of arguments, some of 
which have never been understood by logicians 
until recent years. One important kind of ar- 
gument is known as the Disjunctive Syllo- 
gism, though it does not obey the rules of the 



176 Logical Thinking 

syllogism, or in any way resemble syllo- 
gisms/^ 

The Disjunctive Syllogisml is one having a 
disjunctive proposition in its major premise. 
The disjunctive proposition also appears in 
the conclusion when the disjunction in the ma- 
jor premise happens to contain more than two 
terms. A disjunctive proposition, we have 
seen, is one which possesses alternative predi- 
cates for the subject in which the conjunction 
*^or^^ (sometimes accompanied by ^^ either^') 
appears. As for instance : ^ ^ Lightning is sheet 
or forked ;'' or, ^^ Arches are either round or 
pointed;'^ or, ^^ Angles are either obtuse, or 
right angled, or acute. ' ' The different things 
joined together by ^^or'' are called Alterna- 
<tives, the term indicating that we may choose 
between the things, and that if one will not 
answer our purpose we may take the other, or 
one of the others if there be more than one 
other. 

The Rule regarding the Use of Disjunctive 
Syllogisms is that : ^ ^ If one or more alterna- 
tives be denied, the rest may still be affirmed. ' ' 
Thus if we say that ^ ^ A is B or C, ' ' or that ' ' A 
is either B or C,'' we may deriy the B but still 



Vabieties of Syllogisms 177 

affirm the C, Some airtliorities also hold that 
*^If we affirm one alternative, we must deny 
the remainder,'' but this view is vigorously 
disputed by other authorities. It would seem 
to be a valid rule in cases where the term 
^^ either" appears as: ^* A is either B or C," 
because there seems to be an implication that 
one or the other alone can be true. But in 
cases like : ^ ^ A is B or C, " there may be a pos- 
sibility of both being true. Jevons takes this 
latter view, giving as an example the proposi- 
tion: *^A Magistrate is a Justice-of-the- 
Peace, a Mayor, or a Stipendiary Magis- 
trate,'' but it does not follow that one who is 
a Justice-of-the-Peace may not be at the same 
timie a Mayor. He states: ^^ After affirming 
one alternative we can only deny the others if 
there be such a difference between them thM 
they could not be true at the same time/^ It 
would seem that both contentions are at the 
same time true, the example given by Jevons 
illustrating his contention, and the proposi- 
tion ^^The prisoner is either guilty or inno- 
cent" illustrating the contentions of the other 
side. 
A Dilemma is a conditional syllogism whose 



178 Logical Thinking 

Major Premise presents some sort of alterna- 
tive. Whately defines it as: ^^A conditional 
syllogism with two or more antecedents in the 
major, and a disjunctive minor. '^ There being 
two mutually exclusive propositions in the 
Major Premise, the reasoner is compelled to 
admit one or the other, and is then caught be- 
tween *^the two horns of the dilemma." 



CHAPTER XVIII. 

KEASONING BY AKALOGY 

What is called Reasoning by Analogy is one 
of the most elementary forms of reasoning, 
and the one which the majority of us most fre- 
quently employ. It is a primitive form of 
hasty generalization evidencing in the natural 
expectation that ** things will happen as they 
have happened before in like circumstances. '* 
The term as used in logic has been defined as 
*^ Resemblance of relations; Resemblances of 
any kind on which an argument falling short 
of induction may be founded. ' ' Brooks says : 
^^ Analogy is that process of thought by which 
we infer that if two things resemble each 
other in one or more particulars, they will re- 
semble each other in some other particular.'* 

Jevons states the Rule for Reasoning hy 
Analogy, as follows : *^If two or more things 
resemble each other in many points, they will 
probably resemble each other also in more 
points.'' Others have stated the same prin- 
ciple as follows : ^^ When one thing resembles 

179 



180 Logical Thinking 

another in known particulars, it will resemble 
it also in the unknown;'^ and ^^If two things 
agree in several particulars, they will also 
agree in other particulars.'' 

There is a difference between generalization 
by induction, and by analogy. In inductive 
generalization the rule is: ^^What is true of 
the many is true of all;'' while the rule of 
analogy is: ^^ things that have some things in 
commion have other things in common." As 
Jevons aptly remarks : ^ ' Eeasoning by Anal- 
ogy differs only in degree from that kind of 
reasoning called ^Generalization.' When 
many things resemble each other in a few 
properties, we argue about them by Generali- 
zation. When a few things resemble each 
other in many properties, it is a case of analo- 
gy." Illustrating Analogy, we may say that 
if in A we find the qualities, attributes or 
properties called a, h, c, d, e, f, g, respectively, 
and if we find that in B the qualities, etc., 
called a, b, c, d, e, respectively, are present, 
then we may reason by analogy that the qual- 
ities / and g must also belong to B. 

Brooks says of this form of reasoning: 
' ' This principle is in constant application in 



Eeasoning by Analogy 181 

ordinary life and in science. A physician, in 
visiting a patient, says this disease corres- 
ponds in several particulars with typhoid fe- 
ver, hence it will correspond in all particulars, 
and is typhoid fever. So, when the geologist 
discovers a fossil animal with large, strong, 
blunt claws, he infers that it procured its food 
by scratching or burrowing in the earth. It 
was by analogy that Dr. Buckland constructed 
an aninaal from a few fossil bones, and when 
subsequently the bones of the entire animal 
were discovered, his construction was found 
to be correct." Halleck says: ^^In argu- 
ment or reasoning we are much aided by the 
habit of searching for hidden resemblances. 
. . . The detection of such a relation cul- 
tivates thought. If we are to succeed in argu- 
ment, we must develop what some call a sixth 
sense of such relations. . . . The study 
of poetry may be made very serviceable in de- 
tecting analogies and cultivating the reason- 
ing powers. When the poet brings clearly to 
mind the change due to death, using as an il- 
lustration the caterpillar body transformed 
into the butterfly spirit, moving with winged 
ease over flowering meadows, he is cultivating 



182 LoGiCAx. Thinking 

our apprehension of relations, none the less 
valuable because they are beautiful.'* 

But the student must be on guard against 
the deceptive conclusions sometimes arising 
from Reasoning by Analogy. As Jevons. says : 
^^In many cases Reasoning by Analogy is 
found to be a very uncertain guide. In some 
cases unfortunate mistakes are made. Chil- 
dren are sometimes killed by gathering and 
eating poisonous berries, wrongly inferring 
that they can be eaten, because other berries, 
of a somewhat similar appearance, have been 
found agreeable and harmless. Poisonous 
toadstools are occasionally mistaken for mush- 
rooms, especially by people not accustomed to 
gathering theni. In Norway mushrooms are 
seldom seen, and are not eaten; but when I 
once found a few there and had them cooked 
at an inn, I was amused by the people of the 
inn, who went and collected toadstools and 
wanted me to eat them also. This was clearly 
a case of mistaken reasoning by analogy. 
Even brute animals reason in the same way in 
some degree. The beaten dog fears every 
stick, and there are few dogs which will not 
run away when you pretend to pick up a stone, 



Eeasoning by Analogy 183 

even if there be no stone to pick np. ' ' Halleck 
says: ^^Many false analogies are manufao 
tured, and it is excellent thought training to 
expose them. The majority of people think 
so little that they swallow these false analo- 
gies just as newly fledged robins swallow 
small stones dropped into their open mouths. 
. • . This tendency to think as others do 
must be resisted somewhere along the line, or 
there can be no progress.'* Brooks says: 
^^The argument from Analogy is plausible, 
but often deceptive. Thus to infer that since 
American swans are white, the Australian 
swan is white, gives a false conclusion, for it 
is really black. So to infer that because John 
Smith has a red nose and is a drunkard, then 
Henry Jones who also has a red nose is also a 
drunkard, would be a dangerous inference. 
. . . Conclusions of this kind drawn from 
analogy are frequently fallacious.'' 

Regarding the Rule for Reasoning front 
Analogy, Jevons says: ^^ There is no way in 
which we can really assure ourselves that we 
are arguing safely by analogy. The only rule 
that can be given is this ; that the more closely 
two things resemble each other, the more like- 



184 Logical Thinking 

]y it is that they are the same in other respects, 
especially in points closely connected with 
those observed. . . • In order to be clear 
about our conclusions, we ought in fact never 
to rest satisfied with mere analogy, but ought 
to try to discover the general laws governing 
the case. In analogy we seem to reason from 
one fact to another fact without troubling our- 
selves either with deduction or induction. But 
it is only by a kind of guess that we do so ; it is 
not really conclusive reasoning. We ought 
properly to ascertain what general laws of na- 
ture are shown to exist by the facts observed, 
and then infer what will happen according to 
these laws. . . . We find that reasoning 
by analogy is not to be depended upon, unless 
we make such an inquiry into the causes and 
laws of the things in question, that we really 
employ inductive and deductive reasoning.'^ 
Along the same lines. Brooks says: ^^The 
inference from analogy, like that from induc- 
tion, should be used with caution. Its conclu- 
sion must not be regarded as certain, but 
merely as reaching a high degree of probabil- 
ity. The inference from a part to a part, no 
more than from a part to the whole, is attend- 



Eeasoning by Analogy 185 

ed with any rational necessity. To attain cer- 
tainty, we must show that the principles which 
lie at the root of the process are either neces- 
sary laws of thought or necessary laws of na- 
ture; both of which are impossible. Hence 
analogy can pretend to only a high degree of 
probability. It may even reach a large de- 
gree of certainty, but it never reaches neces- 
sity. "We must, therefore, be careful not to 
accept any inference from analogy as true un- 
til it is proved to be true by actual observation 
and experiment, or by such an application of 
induction as to remiove all reasonable doubt. " 



CHAPTER XIX. 

FALLACIES 

A Fallacy is: ^^An unsound argument or 
mode of arguing, whicfi, while appearing to 
be decisive of a question, is in reality not so ; 
an argument or proposition apparently sound, 
but really fallacious ; a fallacious statement or 
proposition, in which the error is not appar- 
ent, and which is therefore likely to mislead 
or deceive; sophistry.'* 

In Deductive Eeasoning, we meet with two 
classes of Fallacies; namely, (1) Fallacious 
Premise; and (2) Fallacious Conclusion. We 
shall now consider each of these in turn. 

Fallacious Premise is in effect an unwar- 
ranted assumption of premises. One of the 
most common formis of this kind of Fallacy is 
known as ^^ Begging the Question/^ the prin- 
ciple of which is the assumption of a funda- 
mental premise which is not conceded ; the un- 
warrantable assumption of that which is to be 
proved ; or the assumption of that by which it 
is to be proved, without proving it. Its most 

186 



Fallacies 187 

common form is that of boldly stating some un- 
proven fact, authoritatively and positively, 
and then proceeding to use the statement as 
the major premise of the argument, proceed- 
ing logically from that point. The hearer per- 
ceiving the argument proceeding logically oft- 
en fails to remember that the premise has been 
merely assumed, without warrant and without 
proof and omitting the hypothetical ^^if/' 
One may proceed to argue logically from the 
premise that ^^The moon is made of green 
cheese," but the whole argument is invalid 
and fallacious because of the fact that the per- 
son miaking it has '^begged the question" 
upon an unwarranted premise. Hyslop gives 
a good example of this form of fallacy in the 
case of the proposition *^ Church and State 
should be united. ' ' Proof being demanded the 
advocate proceeds to ^^beg the question" as 
follows : ^ ^ Good institutions should be united ; 
Church and State are good institutions ; there- 
fore. Church and State should be united." The 
proposition that ^ ^ Good institutions should be 
united" is fallacious, being merely assumed 
and not proven. The proposition sounds rea- 
sonable, and few will feel disposed to dispute 



188 Logical Thinking 

it at first, but a little consideration will show 
that while some good institutions may well be 
united, it is not a general truth that all should 
be so. 

^^ Begging the Question '' also often arises 
from giving a name to a thing, and then as- 
suming that we have explained the thing. This 
is a very frequent practice with many people 
—they try to explain by merely applying 
names. An example of this kind is had in the 
case of the person who tried to explain why 
one could see through a pane of glass by say- 
ing ^^ because it is transparent." Or when 
one explains that the reason a certain sub- 
stance breaks easily is ^* because it is brittle." 
Moliere makes the father of a dumb girl ask 
why his daughter is dumb. The physician 
answers: ^^ Nothing is more easy than to ex- 
plain it; it comes from her having lost the 
power of speech." ^^Yes, yes," objects the 
father, *^but the cause, if you please, why she 
has lost the power of speech. ^ ' The physician 
gravely replies: ^^AU our best authors will 
tell you tha;t it is the impeding of the action of 
the tongue." 

Jevons says: ^^The most frequent way. 



Fallacies 189 

perhaps, in which we commit this kind of fal- 
lacy is to employ names which imply that we 
disapprove of something, and then argue that 
because it is such and such, it must be con- 
demned. When two sportsmen fall out in 
some manner relating to the subject of game, 
one will, in all probability, argue that the act 
of the other was ^unsportsmanlike, ' and there- 
fore should not have been done. Here is to all 
appearance a correct syllogism: 

^^No unsportsmanlike act should be done; 
John Robinson's act was unsportsmanlike: 
Therefore, John Robinson's act should not 
have been done. 

^^This is quite correct in form; but it is ev- 
idently the mere semblance of an argument. 
^Unsportsmanlike' means what a sportsman 
should not do. The point to be argued was 
whether the act fell within the customary 
definition of what was unsportsmanlike.^^ 

Arising from '^Begging the Question,'' and 
in fact a class of the latter, is what is called 
^'Reasoning in a Circle." In this form of fal- 
lacy one assumes as proof of a proposition the 
proposition itself; or, uses the conclusion to 
prove the premise. For instance : ' ' This man 



190 Logical Thinking 

is a rascal because lie is a rogue ; and lie is a 
rogue because he is a rascal.'' Or, **It is warm 
because it is summer ; and it is suuiimer be- 
cause it is warm.'' Or ^^He never drinks to 
excess, because be is never intemperate in 
drinking." 

Brooks says : **Thus to argue that a party 
is good because it advocates good measures, 
and that certain measures are good because 
they are advocated by so excellent a party, is 
to reason in a circle. So when persons argue 
that their church is the true one, because it 
was established by God, and then argue that 
since it is the true church it must have been 
founded by God, they fall into this fallacy. To 
argue that *the will is determined by the 
strongest motive' and to define the strongest 
motive as *that which influences the will,' is 
to revolve in a circle of thought and prove 
nothing. Plato commits this error when he 
argues the immortality of the soul from its 
simplicity, and afterwards attempts to prove 
its simplicity from its immortality. ' ' It needs 
care to avoid this error, for it is surprising 
how easily one falls into it. Hyslop says : 
*'The fallacy of Eeasoning in a Circle occurs 



Fallacies 191 

mostly in long arguments where it can be com- 
mitted without ready detection. . . . 
When it occurs in a long discourse it may be 
committed without easy discovery. It is like- 
ly to be occasioned by the use of synonyms 
which are taken to express more than the con- 
ception involved when they do not.'' What is 
called a Vicious Circle is caused when the con- 
jclusion of one syllogism is used for a proposi- 
tion in another syllogism, which in its turn 
comes to be used as a basis for the first or 
original syllogism. 

Fallacious Conclusion is in effect an un- 
warranted or irrelevant assumption of a logi- 
cal conclusion. There are many forms of this 
fallacy among which are the following : 

Shifting ground, which consists in the pre- 
tence of proving one thing while in reality 
merely a similar or related thing is being 
proved. In this class is the argument that be- 
cause a man is profane he must necessarily be 
dishonest; or that because a man denies the 
inspiration of the Scriptures he must be an 
atheist. 

Fallacious Questioning, in which two or 
more related questions are asked, and the 



192 Logical Thinking 

answer of one is then applied to tlie other. For 
instance : ' ' You assert that the more civilized a 
commnnity, the more silk-hats are to be found 
in itr' ^^Yes.^' ^^Then, yon state that silk- 
hats are the promoters and cause of civiliza- 
tion in a community T ^ A question of this kind 
is often so arranged that an answer either in 
the aflSrmative or the negative will lead to a 
false or fallacious inference. For instance, 
the question once asked a respectable citizen 
on the witness stand: ^^Have you stopped 
beating your mother T' An answer of either 
*^Yes'^ or ^*No," was out of the question, for 
it would have placed the witness in a false po- 
sition, for he had never beaten his mother, nor 
been accused of the same. 

Partial Proof y in which the proof of a par- 
tial or related fact is used to infer a proof of 
the whole fact or a related one. For instance, 
it is fallacious to argue that a man has been 
guilty of drunkenness by merely proving that 
he was seen entering a saloon. 

Appeal to Public Opinion, in which the prej- 
udices of the public are appealed to rather 
than its judgment or reason. In politics and 



Fallacies 193 

theological argument this fallacy is frequent. 
It is no argument, and is reprehensible. 

Appeal to Authority, or Reverence, in which 
the reverence and respect of the public for cer- 
tain persons is used to influence their feelings 
in place of their judgment or reason. For in- 
stance : ' ' Washington thought so-and-so, and 
therefore it must be right;" or **It is foolish 
to affirm that Aristotle erred;" or ^*It has 
been believed by men for two thousand years, 
that, etc;" or *^What our fathers believed 
must be true." Appeals of this kind may have 
their proper place, but they are fallacies 
nevertheless, and not real argument. 

Appeal to Profession, in which an appeal is 
made to practices, principles or professions of 
the opponent, rather than to reason or judg 
ment. Thus we may argue that a certain phi- 
losophy or religion cannot be sound or good, 
because certain people who hold it are not con- 
sistent, or not worthy, moral or sober. This 
argument is often used effectively against an 
opponent, and is valid against him personally. 
But it is no valid argument against his philos- 
ophy or belief, because he may act in violation 
of them, or he may change his practices and 



194 Logical Thinking 

still adhere to Hs beliefs— the two are not 
joined. 

Appeal to General Belief, in which an ap- 
peal is made to general or universal belief, al- 
though the same may be unsupported by 
proof. This is quite common, but is no real 
argument. The common opinion may be erro- 
neous, as history proves. A few centuries ago 
this argument could have been used in favor 
of the earth being flat, etc. A half-century ago 
it was used against Darwin. Today it is being 
used against other new ideas. It is a fallacy 
by its very nature. 

Appeal to Ignorance, in which an appeal is 
made to the ignorance of the opponent that his 
conviction may follow from his inability to 
prove the contrary. It is virtually no argu- 
ment that: ^^ So-and-so must be true, because 
you cannot prove that it is not/^ As Brooks 
says: ''To argue that there is no material 
world, because we cannot explain how the 
mind knows it to exist, is the celebrated fal- 
lacy of Hume in philosophy. The fact that we 
cannot find a needle in a haystack is no proof 
that it is not there. ^ ' 

Introduction of New Matter, also called Nen 



Fallacies 195 

Sequitur, in which matter is introduced into 
the conclusion that is not in the premises. 
Hyslop gives the following example of it: 
^^AU men are rational; Socrates is a man; 
therefore, Socrates is noble/ ^ De Morgan 
gives the following more complex example: 
^* Episcopacy is of Scripture origin; The 
Church of England is the only Episcopal 
church in England; therefore, the church es- 
tablished is the church that ought to be sup- 
ported.^' 

Other fallacies, resembling in some respects 
those above mentioned, are as follows : 

Fallacy of Ambiguous Terms, in which dif- 
ferent meanings of the same word are used to 
produce the fallacious argument. As Jevons 
says : ^ ^ A word with two distinct meanings is 
really two words/ ^ 

Confusion between Collective and General 
Meanings of a Term, of which Jevons says : 
^^It would be obviously absurd to argue that 
because all the books in the British Museum 
Library are sure to give information about 
King Alfred, therefore any particular book 
will be sure to give it. By ^all the books in the 
British Museum Library,' we mean all taJcen 



196 Logical Thinking 

together. There are many other cases where 
the confusion is not so evident, and where 
great numbers of people are unable to see the 
exact difference. ' ^ 

Arguing froms the Collective to the General, 
in which the fallacy consists of arguing that 
because something is true of the whole of a 
group of things, therefore it is true of any of 
those things. Jevonssays: ^MZZ the soldiers 
in a regiment may be able to capture a town, 
but it is absurd to suppose that therefore 
every soldier in the regiment could capture 
the town single handed. White sheep eat a 
great deal more than black sheep; but that is 
because there are so many more of them.^' 

Uncertain Meaning of a Sentence, from 
which confusion arises and fallacious argu- 
ment may spring. Jevons says : ^ ' There is a 
humorous way of proving that a cat must have 
three tails : Because a cat has one tail more 
than no cat ; and no cat has two tails ; there- 
fore, any cat has three tails/' Here the fal- 
lacy rests upon a punning interpretation of 
''no.'' 

Proving the Wrong Conclusion, in which the 
attempt to confuse conclusions is made, with 



Fallacies 197 

the result that some people will imagine that 
the case is established. Jevons says : ' ' This 
was the device of the Irishman, who was 
charged with theft on the evidence of three 
witnesses, who had seen him do it; he pro- 
posed to call thirty witnesses who had not seen 
him do it. Equally logical was the defense of 
the mian who was called a materialist, and who 
replied, ^I am not a materialist; I am a bar- 
ber.^ '' 

Fallacy of Unsuccessful Argument, irxwhioh 
is attempted the illogical conclusion that be- 
cause a certain argument has failed the oppo- 
site conclusion is proven. This fallacy is quite 
common, especially in cases of juries. One 
side fails to prove certain contentions, and the 
jury leaps to the conclusion that the opposite 
contention must be correct. This is clearly 
fallacious, for there is always the possibility 
of a third explanation. In the case of a claim 
of alibi juries are apt to fall into this fallacy. 
The failure of the attempt to establish an alibi 
is often held to be in the nature of proof of the 
guilt of the accused. Old trial lawyers assert 
that a failure to establish a claimed alibi tends 
to injure the chance of the accused more than 



198 Logical Thinking 

direct evidence against him. Yet, as all logi- 
cal reasoners will see, there is no logical valid- 
ity in any such inference. As Jevons has well 
said: ^^No number of failures in attempting 
to prove a proposition really disprove it J' At 
the end of each failure the case simply stands 
in the same position rs before the attempt; 
i. 6./^ not proven/' 

All Violations of the Rules of the Syllogism 
constitute fallacies, as may be seen by forming 
a syllogism in violation of one or more of the 
rules. 

The logicians, particularly those of ancient 
times, took great pains to discover and name 
new variations of fallacies, many of which 
were hair-splitting in nature, and not worthy 
of being considered seriously. Some of those 
which we have enumerated may possibly be 
open to the same criticism, but we have omit- 
ted many of the worst offenders against prac- 
tical common sense. An understanding of the 
fundamental Laws of Eeasoning is sufficient 
to expose and unmask all fallacies, and such 
understanding is far more valuable than the 
memorizing of the names of hair-splitting fal- 
lacies which would not deceive a child. 



Fallacies 199 

In addition to the above stated fallacies of 
Deductive Eeasoning, there are other fallacies 
which are met with in Inductive Reasoning. 
Let us briefly consider them. 

Hasty and False Generalization is a com- 
mon fallacy of this class. Persons sometimes 
see certain qualities in a few individuals of a 
class, and mistakenly infer that all the indi- 
viduals in that class must possess these same 
qualities. Travelers frequently commit this 
fallacy. Englishmen visiting the United 
States for a few weeks have been known to 
publish books upon their return home making 
the most ridiculous generalizations regarding 
the American people, their assertions being 
based upon the observation of a few scattered 
individuals, often not at all representative. 
Americans traveling abroad commit similar 
errors. A flying trip through a country does 
not afford the proper opportunity for correct 
generalization. As Brooks says: ^*No hy- 
pothesis should be accepted as true until the 
facts are so numerous that there can be no 
doubt of its being proved.'* 

Fallacies of Observation result from incor- 
rect methods of observation among which may 



200 Logical Thinking 

be mentiotLed the following: (1) Careless Ob- 
servation, or inexact perception and concep- 
tion ; (2) Partial Observation, in which one ob- 
serves only a part of the thin^ or fact, omit- 
ting the remainder, and thus forming an in- 
complete and imperfect concept of the thing 
or fact; (3) Neglect of Exceptions and Con- 
tradictory Facts, in which the exceptions and 
contradictory facts are ignored, thereby giv- 
ing undue importance to the observed facts ; 
(4) Assumption of Facts which are not real 
facts, or the assumption of the truth of things 
which are untrue; (5) Confusing of Inferences 
with Facts, which is most unwarrantable. 

Fallacies of Mistaken Cause result from th^ 
assum|)tion of a thing as a cause, when it is not 
so, of which the following are familiar esatn- 
ptes: Substituting the Antecedent for the 
Cause, which consists in assuming a mere an- 
tecedent thing for a cause of another thing. 
Thus one might assume that the crowing of 
the cock was the cause of daybreak, because it 
preceded it ; or that a comet was the cause of 
the plague which followed its appearance ; or 
in the actual case in which a child reasoned 
that doctors caused deaths, because observa- 



Fallacies 201 

tion had shown tliat they always visited per- 
sons before they died ; or that crops failed be- 
cause a President of a certain political party 
had been inangnrated a few months before. 
Some fallacies of everyday reasoning are 
quite as illogical as those just mentioned. Sub- 
stituting the Symptom for the Cause, which 
consists in assuming as a cause some mere 
symptom, sign or incident of the real cause. 
To assume that the pimples of measles were 
the cause of the disease, would be to commit a 
fallacy of this kind. We have mentioned else- 
where the fallacy which would assume silk- 
hats to be the cause of Civilizaiton, instead of 
being a mere incident of the latter. Politicians 
are fond of assuming certain incidents or 
signs of a period, as being the causes of the 
prosperity, culture and advancement of the 
period, or the reverse. One might argue, with 
equal force, that automobiles were the causes 
of national prosperity, pointing to the fact 
that the more automobiles to be seen the better 
the times. Or, that straw hats produced hot 
weather, for similar reasons. 

The Fallacy of Analogy consists in assum- 
ing a resemblance or identity, where none ex- 



W ^^3 3 4 : 

202 Logical Thinking 

ists. We have spoken of this in another chap- 
ter. Brooks says, also: ^^It is a fallacy to 
carry an analogy too far ; as to infer from the 
parable of the praying of the importunate 
woman that God resembles the unjust judge. '^ 
In conclusion, we would call your attention 
to the following words from Jevons, in which 
he expresses the gist of the matter : ^ ^ It is im- 
possible too often to remind people that, on 
the one hand, all correct reasoning consists in 
substituting like things for like things^ and in- 
ferring that what is true of one will be true of 
all which are similar to it in the points of re- 
semblance concerned in the matter. On the 
other hand, all incorrect reasoning consists in 
putting one thing for another where there is 
not the requisite likeness. It is the purpose of 
the rules of deductive and inductive logic to 
enable us to judge as far as possible when we 
are thus rightly or wrongly reasoning from 
some things to others. '' 

FINIS. 



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